SUMMER REVIEW for students entering GEOMETRY REMEMBER: Your high school mathematics courses require you to use concepts learned in previous math classes. Use this Summer Review to review skills that you will need to be successful in geometry. Surfs up! Make waves with math!
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SUMMER REVIEW for students entering GEOMETRY REMEMBER: Your high school mathematics courses require you to use concepts learned in previous math classes.
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SUMMER REVIEW for students entering
GEOMETRYREMEMBER Your high school mathematics courses require you to use concepts learned in previous math classes Use this Summer Review to review skills that you will need to be successful in geometry
Surfs up Make waves with math
Give two ways to write each algebraic expression
in wordsNOTE Answers will vary
1 x + 3 2 2m ndash 7 3 5y
041923 Mrs McConaughy Geometry
2
Possible phrases for each of the previous expressions
1 3 more than a number a number increased by 32 7 less than twice a number twice a number decreased by 7
3 5 times a number
Evaluate each expression for
x = 8 y = 5 and z = 44 x + y 8 + 5 135 xz 84 2041923 Mrs McConaughy
Geometry3
Evaluate each expression
6 (-2)3
-8 49
22
3
041923 Mrs McConaughy Geometry
4
Find each square root
8
9
36
49
041923 Mrs McConaughy Geometry
5
Time to recall your
perfect squares
8
9
-6
7
Write all classifications that apply to each real number (natural whole integer rational irrational)
26The ratio of band members to non-band members in Seneca Valley Intermediate High School is 25 There are 875 students in grades 9 and 10 How many band members are there
27 Seneca Valley track star I M Fleetfeet ran at a rate of 6 mih What is this speed in milesminute
041923 Mrs McConaughy Geometry
9
250 band members 625 non- band members
110 mileminute or 1 mileminute
Solve each inequality and graph on a number line
28 18 + 2x le 50 x le 16 16
29 7 ndash 2t le 21 t ge - 7 -7
041923 Mrs McConaughy Geometry
10
RecallRULE When multiplying or dividing an inequality by a negative number always reverse the symbol of inequality
Find the slope of each line
30 31
041923 Mrs McConaughy Geometry
11
m = 0 Slope m is undefined
Find the slope of the line containing the given points
32 (12) amp (7 -2)
33 (- 410) amp (03)
Time to cool off with ski
bird
041923 Mrs McConaughy Geometry
12
m = -2 ndash 2 7 - 1 = -46 = -23
m = 10 ndash 3 -4 - 0 = 7-4
Graph each equation
34 y = -2
35 x = 4
36 y = - frac12 x + 4
37 y = 5x - 3
NOTE Remember to label your lines
041923 Mrs McConaughy Geometry
13
Write the equation of the line in slope-intercept form
38slope = frac12 y-intercept = -5
39 slope = -3 y-intercept = 0
40 through the points (1-4) and (32)
041923 Mrs McConaughy Geometry
14
y = mx + b y = 12x - 5
y = mx + b y = -3x
Step 1 Find slope m Step 2 Use point- slope form of a line
y = 3x - 7
41 Find the x and y intercepts of -2x + 4y = 7 x-intercept (-72 0) y-intercept (0 74)42 Is the point (4 14) on the line y = -3x + 2
Explain No because when substituting x and y values into
the equation y = -3x + 2 your final equation is 14 = -10 which is false since 14 ne -10
43 Solve the system of equations by graphing y = x ndash 3 y = -x + 1
041923 Mrs McConaughy Geometry
15
HINT Step 1 Graph each line on the coordinate plane using slope-intercept method Step 2 Find the coordinates of the point of intersection
SimplifyRecall Basic Rules for Exponents
44 25 middot 26 45 (25)6
2 11 or 2048 230
46 a4 middot b2 middot a5 47 (4x2y6)(-2x3y4)2
a9 b2 16x8y14
48 33 or 27 49 3ab5
5
2
3
3
5 9
4 4
6
2
a b
a b
041923 Mrs McConaughy Geometry
16
Evaluate each function for the given input value
50 For y = 2x + 10 find y when x = 6
51 For y = frac12 t ndash 3 find y when t = 12
041923 Mrs McConaughy Geometry
17
Y = 2(6) + 10Y = 12+ 10
Y = 22
Y = frac12 (12) -3Y = 6-3
Y = 3
Evaluate the exponential function
52 The function y = 2(3)x models an insect population after x days What will the population be on the 5th day
26The ratio of band members to non-band members in Seneca Valley Intermediate High School is 25 There are 875 students in grades 9 and 10 How many band members are there
27 Seneca Valley track star I M Fleetfeet ran at a rate of 6 mih What is this speed in milesminute
041923 Mrs McConaughy Geometry
9
250 band members 625 non- band members
110 mileminute or 1 mileminute
Solve each inequality and graph on a number line
28 18 + 2x le 50 x le 16 16
29 7 ndash 2t le 21 t ge - 7 -7
041923 Mrs McConaughy Geometry
10
RecallRULE When multiplying or dividing an inequality by a negative number always reverse the symbol of inequality
Find the slope of each line
30 31
041923 Mrs McConaughy Geometry
11
m = 0 Slope m is undefined
Find the slope of the line containing the given points
32 (12) amp (7 -2)
33 (- 410) amp (03)
Time to cool off with ski
bird
041923 Mrs McConaughy Geometry
12
m = -2 ndash 2 7 - 1 = -46 = -23
m = 10 ndash 3 -4 - 0 = 7-4
Graph each equation
34 y = -2
35 x = 4
36 y = - frac12 x + 4
37 y = 5x - 3
NOTE Remember to label your lines
041923 Mrs McConaughy Geometry
13
Write the equation of the line in slope-intercept form
38slope = frac12 y-intercept = -5
39 slope = -3 y-intercept = 0
40 through the points (1-4) and (32)
041923 Mrs McConaughy Geometry
14
y = mx + b y = 12x - 5
y = mx + b y = -3x
Step 1 Find slope m Step 2 Use point- slope form of a line
y = 3x - 7
41 Find the x and y intercepts of -2x + 4y = 7 x-intercept (-72 0) y-intercept (0 74)42 Is the point (4 14) on the line y = -3x + 2
Explain No because when substituting x and y values into
the equation y = -3x + 2 your final equation is 14 = -10 which is false since 14 ne -10
43 Solve the system of equations by graphing y = x ndash 3 y = -x + 1
041923 Mrs McConaughy Geometry
15
HINT Step 1 Graph each line on the coordinate plane using slope-intercept method Step 2 Find the coordinates of the point of intersection
SimplifyRecall Basic Rules for Exponents
44 25 middot 26 45 (25)6
2 11 or 2048 230
46 a4 middot b2 middot a5 47 (4x2y6)(-2x3y4)2
a9 b2 16x8y14
48 33 or 27 49 3ab5
5
2
3
3
5 9
4 4
6
2
a b
a b
041923 Mrs McConaughy Geometry
16
Evaluate each function for the given input value
50 For y = 2x + 10 find y when x = 6
51 For y = frac12 t ndash 3 find y when t = 12
041923 Mrs McConaughy Geometry
17
Y = 2(6) + 10Y = 12+ 10
Y = 22
Y = frac12 (12) -3Y = 6-3
Y = 3
Evaluate the exponential function
52 The function y = 2(3)x models an insect population after x days What will the population be on the 5th day
26The ratio of band members to non-band members in Seneca Valley Intermediate High School is 25 There are 875 students in grades 9 and 10 How many band members are there
27 Seneca Valley track star I M Fleetfeet ran at a rate of 6 mih What is this speed in milesminute
041923 Mrs McConaughy Geometry
9
250 band members 625 non- band members
110 mileminute or 1 mileminute
Solve each inequality and graph on a number line
28 18 + 2x le 50 x le 16 16
29 7 ndash 2t le 21 t ge - 7 -7
041923 Mrs McConaughy Geometry
10
RecallRULE When multiplying or dividing an inequality by a negative number always reverse the symbol of inequality
Find the slope of each line
30 31
041923 Mrs McConaughy Geometry
11
m = 0 Slope m is undefined
Find the slope of the line containing the given points
32 (12) amp (7 -2)
33 (- 410) amp (03)
Time to cool off with ski
bird
041923 Mrs McConaughy Geometry
12
m = -2 ndash 2 7 - 1 = -46 = -23
m = 10 ndash 3 -4 - 0 = 7-4
Graph each equation
34 y = -2
35 x = 4
36 y = - frac12 x + 4
37 y = 5x - 3
NOTE Remember to label your lines
041923 Mrs McConaughy Geometry
13
Write the equation of the line in slope-intercept form
38slope = frac12 y-intercept = -5
39 slope = -3 y-intercept = 0
40 through the points (1-4) and (32)
041923 Mrs McConaughy Geometry
14
y = mx + b y = 12x - 5
y = mx + b y = -3x
Step 1 Find slope m Step 2 Use point- slope form of a line
y = 3x - 7
41 Find the x and y intercepts of -2x + 4y = 7 x-intercept (-72 0) y-intercept (0 74)42 Is the point (4 14) on the line y = -3x + 2
Explain No because when substituting x and y values into
the equation y = -3x + 2 your final equation is 14 = -10 which is false since 14 ne -10
43 Solve the system of equations by graphing y = x ndash 3 y = -x + 1
041923 Mrs McConaughy Geometry
15
HINT Step 1 Graph each line on the coordinate plane using slope-intercept method Step 2 Find the coordinates of the point of intersection
SimplifyRecall Basic Rules for Exponents
44 25 middot 26 45 (25)6
2 11 or 2048 230
46 a4 middot b2 middot a5 47 (4x2y6)(-2x3y4)2
a9 b2 16x8y14
48 33 or 27 49 3ab5
5
2
3
3
5 9
4 4
6
2
a b
a b
041923 Mrs McConaughy Geometry
16
Evaluate each function for the given input value
50 For y = 2x + 10 find y when x = 6
51 For y = frac12 t ndash 3 find y when t = 12
041923 Mrs McConaughy Geometry
17
Y = 2(6) + 10Y = 12+ 10
Y = 22
Y = frac12 (12) -3Y = 6-3
Y = 3
Evaluate the exponential function
52 The function y = 2(3)x models an insect population after x days What will the population be on the 5th day
26The ratio of band members to non-band members in Seneca Valley Intermediate High School is 25 There are 875 students in grades 9 and 10 How many band members are there
27 Seneca Valley track star I M Fleetfeet ran at a rate of 6 mih What is this speed in milesminute
041923 Mrs McConaughy Geometry
9
250 band members 625 non- band members
110 mileminute or 1 mileminute
Solve each inequality and graph on a number line
28 18 + 2x le 50 x le 16 16
29 7 ndash 2t le 21 t ge - 7 -7
041923 Mrs McConaughy Geometry
10
RecallRULE When multiplying or dividing an inequality by a negative number always reverse the symbol of inequality
Find the slope of each line
30 31
041923 Mrs McConaughy Geometry
11
m = 0 Slope m is undefined
Find the slope of the line containing the given points
32 (12) amp (7 -2)
33 (- 410) amp (03)
Time to cool off with ski
bird
041923 Mrs McConaughy Geometry
12
m = -2 ndash 2 7 - 1 = -46 = -23
m = 10 ndash 3 -4 - 0 = 7-4
Graph each equation
34 y = -2
35 x = 4
36 y = - frac12 x + 4
37 y = 5x - 3
NOTE Remember to label your lines
041923 Mrs McConaughy Geometry
13
Write the equation of the line in slope-intercept form
38slope = frac12 y-intercept = -5
39 slope = -3 y-intercept = 0
40 through the points (1-4) and (32)
041923 Mrs McConaughy Geometry
14
y = mx + b y = 12x - 5
y = mx + b y = -3x
Step 1 Find slope m Step 2 Use point- slope form of a line
y = 3x - 7
41 Find the x and y intercepts of -2x + 4y = 7 x-intercept (-72 0) y-intercept (0 74)42 Is the point (4 14) on the line y = -3x + 2
Explain No because when substituting x and y values into
the equation y = -3x + 2 your final equation is 14 = -10 which is false since 14 ne -10
43 Solve the system of equations by graphing y = x ndash 3 y = -x + 1
041923 Mrs McConaughy Geometry
15
HINT Step 1 Graph each line on the coordinate plane using slope-intercept method Step 2 Find the coordinates of the point of intersection
SimplifyRecall Basic Rules for Exponents
44 25 middot 26 45 (25)6
2 11 or 2048 230
46 a4 middot b2 middot a5 47 (4x2y6)(-2x3y4)2
a9 b2 16x8y14
48 33 or 27 49 3ab5
5
2
3
3
5 9
4 4
6
2
a b
a b
041923 Mrs McConaughy Geometry
16
Evaluate each function for the given input value
50 For y = 2x + 10 find y when x = 6
51 For y = frac12 t ndash 3 find y when t = 12
041923 Mrs McConaughy Geometry
17
Y = 2(6) + 10Y = 12+ 10
Y = 22
Y = frac12 (12) -3Y = 6-3
Y = 3
Evaluate the exponential function
52 The function y = 2(3)x models an insect population after x days What will the population be on the 5th day
26The ratio of band members to non-band members in Seneca Valley Intermediate High School is 25 There are 875 students in grades 9 and 10 How many band members are there
27 Seneca Valley track star I M Fleetfeet ran at a rate of 6 mih What is this speed in milesminute
041923 Mrs McConaughy Geometry
9
250 band members 625 non- band members
110 mileminute or 1 mileminute
Solve each inequality and graph on a number line
28 18 + 2x le 50 x le 16 16
29 7 ndash 2t le 21 t ge - 7 -7
041923 Mrs McConaughy Geometry
10
RecallRULE When multiplying or dividing an inequality by a negative number always reverse the symbol of inequality
Find the slope of each line
30 31
041923 Mrs McConaughy Geometry
11
m = 0 Slope m is undefined
Find the slope of the line containing the given points
32 (12) amp (7 -2)
33 (- 410) amp (03)
Time to cool off with ski
bird
041923 Mrs McConaughy Geometry
12
m = -2 ndash 2 7 - 1 = -46 = -23
m = 10 ndash 3 -4 - 0 = 7-4
Graph each equation
34 y = -2
35 x = 4
36 y = - frac12 x + 4
37 y = 5x - 3
NOTE Remember to label your lines
041923 Mrs McConaughy Geometry
13
Write the equation of the line in slope-intercept form
38slope = frac12 y-intercept = -5
39 slope = -3 y-intercept = 0
40 through the points (1-4) and (32)
041923 Mrs McConaughy Geometry
14
y = mx + b y = 12x - 5
y = mx + b y = -3x
Step 1 Find slope m Step 2 Use point- slope form of a line
y = 3x - 7
41 Find the x and y intercepts of -2x + 4y = 7 x-intercept (-72 0) y-intercept (0 74)42 Is the point (4 14) on the line y = -3x + 2
Explain No because when substituting x and y values into
the equation y = -3x + 2 your final equation is 14 = -10 which is false since 14 ne -10
43 Solve the system of equations by graphing y = x ndash 3 y = -x + 1
041923 Mrs McConaughy Geometry
15
HINT Step 1 Graph each line on the coordinate plane using slope-intercept method Step 2 Find the coordinates of the point of intersection
SimplifyRecall Basic Rules for Exponents
44 25 middot 26 45 (25)6
2 11 or 2048 230
46 a4 middot b2 middot a5 47 (4x2y6)(-2x3y4)2
a9 b2 16x8y14
48 33 or 27 49 3ab5
5
2
3
3
5 9
4 4
6
2
a b
a b
041923 Mrs McConaughy Geometry
16
Evaluate each function for the given input value
50 For y = 2x + 10 find y when x = 6
51 For y = frac12 t ndash 3 find y when t = 12
041923 Mrs McConaughy Geometry
17
Y = 2(6) + 10Y = 12+ 10
Y = 22
Y = frac12 (12) -3Y = 6-3
Y = 3
Evaluate the exponential function
52 The function y = 2(3)x models an insect population after x days What will the population be on the 5th day
26The ratio of band members to non-band members in Seneca Valley Intermediate High School is 25 There are 875 students in grades 9 and 10 How many band members are there
27 Seneca Valley track star I M Fleetfeet ran at a rate of 6 mih What is this speed in milesminute
041923 Mrs McConaughy Geometry
9
250 band members 625 non- band members
110 mileminute or 1 mileminute
Solve each inequality and graph on a number line
28 18 + 2x le 50 x le 16 16
29 7 ndash 2t le 21 t ge - 7 -7
041923 Mrs McConaughy Geometry
10
RecallRULE When multiplying or dividing an inequality by a negative number always reverse the symbol of inequality
Find the slope of each line
30 31
041923 Mrs McConaughy Geometry
11
m = 0 Slope m is undefined
Find the slope of the line containing the given points
32 (12) amp (7 -2)
33 (- 410) amp (03)
Time to cool off with ski
bird
041923 Mrs McConaughy Geometry
12
m = -2 ndash 2 7 - 1 = -46 = -23
m = 10 ndash 3 -4 - 0 = 7-4
Graph each equation
34 y = -2
35 x = 4
36 y = - frac12 x + 4
37 y = 5x - 3
NOTE Remember to label your lines
041923 Mrs McConaughy Geometry
13
Write the equation of the line in slope-intercept form
38slope = frac12 y-intercept = -5
39 slope = -3 y-intercept = 0
40 through the points (1-4) and (32)
041923 Mrs McConaughy Geometry
14
y = mx + b y = 12x - 5
y = mx + b y = -3x
Step 1 Find slope m Step 2 Use point- slope form of a line
y = 3x - 7
41 Find the x and y intercepts of -2x + 4y = 7 x-intercept (-72 0) y-intercept (0 74)42 Is the point (4 14) on the line y = -3x + 2
Explain No because when substituting x and y values into
the equation y = -3x + 2 your final equation is 14 = -10 which is false since 14 ne -10
43 Solve the system of equations by graphing y = x ndash 3 y = -x + 1
041923 Mrs McConaughy Geometry
15
HINT Step 1 Graph each line on the coordinate plane using slope-intercept method Step 2 Find the coordinates of the point of intersection
SimplifyRecall Basic Rules for Exponents
44 25 middot 26 45 (25)6
2 11 or 2048 230
46 a4 middot b2 middot a5 47 (4x2y6)(-2x3y4)2
a9 b2 16x8y14
48 33 or 27 49 3ab5
5
2
3
3
5 9
4 4
6
2
a b
a b
041923 Mrs McConaughy Geometry
16
Evaluate each function for the given input value
50 For y = 2x + 10 find y when x = 6
51 For y = frac12 t ndash 3 find y when t = 12
041923 Mrs McConaughy Geometry
17
Y = 2(6) + 10Y = 12+ 10
Y = 22
Y = frac12 (12) -3Y = 6-3
Y = 3
Evaluate the exponential function
52 The function y = 2(3)x models an insect population after x days What will the population be on the 5th day
26The ratio of band members to non-band members in Seneca Valley Intermediate High School is 25 There are 875 students in grades 9 and 10 How many band members are there
27 Seneca Valley track star I M Fleetfeet ran at a rate of 6 mih What is this speed in milesminute
041923 Mrs McConaughy Geometry
9
250 band members 625 non- band members
110 mileminute or 1 mileminute
Solve each inequality and graph on a number line
28 18 + 2x le 50 x le 16 16
29 7 ndash 2t le 21 t ge - 7 -7
041923 Mrs McConaughy Geometry
10
RecallRULE When multiplying or dividing an inequality by a negative number always reverse the symbol of inequality
Find the slope of each line
30 31
041923 Mrs McConaughy Geometry
11
m = 0 Slope m is undefined
Find the slope of the line containing the given points
32 (12) amp (7 -2)
33 (- 410) amp (03)
Time to cool off with ski
bird
041923 Mrs McConaughy Geometry
12
m = -2 ndash 2 7 - 1 = -46 = -23
m = 10 ndash 3 -4 - 0 = 7-4
Graph each equation
34 y = -2
35 x = 4
36 y = - frac12 x + 4
37 y = 5x - 3
NOTE Remember to label your lines
041923 Mrs McConaughy Geometry
13
Write the equation of the line in slope-intercept form
38slope = frac12 y-intercept = -5
39 slope = -3 y-intercept = 0
40 through the points (1-4) and (32)
041923 Mrs McConaughy Geometry
14
y = mx + b y = 12x - 5
y = mx + b y = -3x
Step 1 Find slope m Step 2 Use point- slope form of a line
y = 3x - 7
41 Find the x and y intercepts of -2x + 4y = 7 x-intercept (-72 0) y-intercept (0 74)42 Is the point (4 14) on the line y = -3x + 2
Explain No because when substituting x and y values into
the equation y = -3x + 2 your final equation is 14 = -10 which is false since 14 ne -10
43 Solve the system of equations by graphing y = x ndash 3 y = -x + 1
041923 Mrs McConaughy Geometry
15
HINT Step 1 Graph each line on the coordinate plane using slope-intercept method Step 2 Find the coordinates of the point of intersection
SimplifyRecall Basic Rules for Exponents
44 25 middot 26 45 (25)6
2 11 or 2048 230
46 a4 middot b2 middot a5 47 (4x2y6)(-2x3y4)2
a9 b2 16x8y14
48 33 or 27 49 3ab5
5
2
3
3
5 9
4 4
6
2
a b
a b
041923 Mrs McConaughy Geometry
16
Evaluate each function for the given input value
50 For y = 2x + 10 find y when x = 6
51 For y = frac12 t ndash 3 find y when t = 12
041923 Mrs McConaughy Geometry
17
Y = 2(6) + 10Y = 12+ 10
Y = 22
Y = frac12 (12) -3Y = 6-3
Y = 3
Evaluate the exponential function
52 The function y = 2(3)x models an insect population after x days What will the population be on the 5th day
26The ratio of band members to non-band members in Seneca Valley Intermediate High School is 25 There are 875 students in grades 9 and 10 How many band members are there
27 Seneca Valley track star I M Fleetfeet ran at a rate of 6 mih What is this speed in milesminute
041923 Mrs McConaughy Geometry
9
250 band members 625 non- band members
110 mileminute or 1 mileminute
Solve each inequality and graph on a number line
28 18 + 2x le 50 x le 16 16
29 7 ndash 2t le 21 t ge - 7 -7
041923 Mrs McConaughy Geometry
10
RecallRULE When multiplying or dividing an inequality by a negative number always reverse the symbol of inequality
Find the slope of each line
30 31
041923 Mrs McConaughy Geometry
11
m = 0 Slope m is undefined
Find the slope of the line containing the given points
32 (12) amp (7 -2)
33 (- 410) amp (03)
Time to cool off with ski
bird
041923 Mrs McConaughy Geometry
12
m = -2 ndash 2 7 - 1 = -46 = -23
m = 10 ndash 3 -4 - 0 = 7-4
Graph each equation
34 y = -2
35 x = 4
36 y = - frac12 x + 4
37 y = 5x - 3
NOTE Remember to label your lines
041923 Mrs McConaughy Geometry
13
Write the equation of the line in slope-intercept form
38slope = frac12 y-intercept = -5
39 slope = -3 y-intercept = 0
40 through the points (1-4) and (32)
041923 Mrs McConaughy Geometry
14
y = mx + b y = 12x - 5
y = mx + b y = -3x
Step 1 Find slope m Step 2 Use point- slope form of a line
y = 3x - 7
41 Find the x and y intercepts of -2x + 4y = 7 x-intercept (-72 0) y-intercept (0 74)42 Is the point (4 14) on the line y = -3x + 2
Explain No because when substituting x and y values into
the equation y = -3x + 2 your final equation is 14 = -10 which is false since 14 ne -10
43 Solve the system of equations by graphing y = x ndash 3 y = -x + 1
041923 Mrs McConaughy Geometry
15
HINT Step 1 Graph each line on the coordinate plane using slope-intercept method Step 2 Find the coordinates of the point of intersection
SimplifyRecall Basic Rules for Exponents
44 25 middot 26 45 (25)6
2 11 or 2048 230
46 a4 middot b2 middot a5 47 (4x2y6)(-2x3y4)2
a9 b2 16x8y14
48 33 or 27 49 3ab5
5
2
3
3
5 9
4 4
6
2
a b
a b
041923 Mrs McConaughy Geometry
16
Evaluate each function for the given input value
50 For y = 2x + 10 find y when x = 6
51 For y = frac12 t ndash 3 find y when t = 12
041923 Mrs McConaughy Geometry
17
Y = 2(6) + 10Y = 12+ 10
Y = 22
Y = frac12 (12) -3Y = 6-3
Y = 3
Evaluate the exponential function
52 The function y = 2(3)x models an insect population after x days What will the population be on the 5th day
Give two ways to write each algebraic expression in words
Evaluate each expression for x = 8 y = 5 and z = 4
Evaluate each expression
Find each square root
Write all classifications that apply to each real number (natural whole integer rational irrational)
Simplify each expression
Solve each equation
Write and solve each proportion
Solve each inequality and graph on a number line
Find the slope of each line
Find the slope of the line containing the given points
Graph each equation
Write the equation of the line in slope-intercept form
PowerPoint Presentation
Simplify Recall Basic Rules for Exponents
Evaluate each function for the given input value
Evaluate the exponential function
Add or subtract the polynomials
Multiply
Factor completely
Yoursquore finished
Write and solve each proportion
26The ratio of band members to non-band members in Seneca Valley Intermediate High School is 25 There are 875 students in grades 9 and 10 How many band members are there
27 Seneca Valley track star I M Fleetfeet ran at a rate of 6 mih What is this speed in milesminute
041923 Mrs McConaughy Geometry
9
250 band members 625 non- band members
110 mileminute or 1 mileminute
Solve each inequality and graph on a number line
28 18 + 2x le 50 x le 16 16
29 7 ndash 2t le 21 t ge - 7 -7
041923 Mrs McConaughy Geometry
10
RecallRULE When multiplying or dividing an inequality by a negative number always reverse the symbol of inequality
Find the slope of each line
30 31
041923 Mrs McConaughy Geometry
11
m = 0 Slope m is undefined
Find the slope of the line containing the given points
32 (12) amp (7 -2)
33 (- 410) amp (03)
Time to cool off with ski
bird
041923 Mrs McConaughy Geometry
12
m = -2 ndash 2 7 - 1 = -46 = -23
m = 10 ndash 3 -4 - 0 = 7-4
Graph each equation
34 y = -2
35 x = 4
36 y = - frac12 x + 4
37 y = 5x - 3
NOTE Remember to label your lines
041923 Mrs McConaughy Geometry
13
Write the equation of the line in slope-intercept form
38slope = frac12 y-intercept = -5
39 slope = -3 y-intercept = 0
40 through the points (1-4) and (32)
041923 Mrs McConaughy Geometry
14
y = mx + b y = 12x - 5
y = mx + b y = -3x
Step 1 Find slope m Step 2 Use point- slope form of a line
y = 3x - 7
41 Find the x and y intercepts of -2x + 4y = 7 x-intercept (-72 0) y-intercept (0 74)42 Is the point (4 14) on the line y = -3x + 2
Explain No because when substituting x and y values into
the equation y = -3x + 2 your final equation is 14 = -10 which is false since 14 ne -10
43 Solve the system of equations by graphing y = x ndash 3 y = -x + 1
041923 Mrs McConaughy Geometry
15
HINT Step 1 Graph each line on the coordinate plane using slope-intercept method Step 2 Find the coordinates of the point of intersection
SimplifyRecall Basic Rules for Exponents
44 25 middot 26 45 (25)6
2 11 or 2048 230
46 a4 middot b2 middot a5 47 (4x2y6)(-2x3y4)2
a9 b2 16x8y14
48 33 or 27 49 3ab5
5
2
3
3
5 9
4 4
6
2
a b
a b
041923 Mrs McConaughy Geometry
16
Evaluate each function for the given input value
50 For y = 2x + 10 find y when x = 6
51 For y = frac12 t ndash 3 find y when t = 12
041923 Mrs McConaughy Geometry
17
Y = 2(6) + 10Y = 12+ 10
Y = 22
Y = frac12 (12) -3Y = 6-3
Y = 3
Evaluate the exponential function
52 The function y = 2(3)x models an insect population after x days What will the population be on the 5th day