• point-slope form • Write the equation of a line in point- slope form. • Write linear equations in different forms.
Feb 06, 2016
• point-slope form
• Write the equation of a line in point-slope form.
• Write linear equations in different forms.
Write an Equation Given Slope and a Point
(x1, y1) = (–2, 0)
Point-slopeform
Simplify.
Answer:
Write the point-slope form of an
equation for a line that passes
through (–2, 0) with slope
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. y – 4 = –2 (x + 3)
B. y + 3 = –2 (x – 4)
C. y – 3 = –2 (x – 4)
D. y + 4 = –2 (x – 3)
Write the point-slope form of an equation for a line that passes through (4, –3) with slope –2.
Write an Equation of a Horizontal Line
Write the point-slope form of an equation for a horizontal line that passes through (0, 5).
Answer: The equation is y – 5 = 0.
(x1, y1) = (0, 5)
Point-slopeform
Simplify.
y – 5 = 0 (x – 0)
y – y1 = m(x – x1)
y – 5 = 0
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. y + 4 = 0
B. y + 3 = 0
C. y – 4 = 0
D. x + 3 = 0
Write the point-slope form of an equation for a horizontal line that passes through (–3, –4).
Write an Equation in Standard Form
In standard form, the variables are on the left side of the equation. A, B, and C are all integers.
Multiply each side by 4 to eliminate the fraction.
Original equation
Distributive Property
Write an Equation in Standard Form
4y – 3x = 3x – 20 – 3x
–3x + 4y = –20
Answer: The standard form of the equation is –3x + 4y = –20 or 3x – 4y = 20.
Simplify.
Subtract 3x from each side.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. –2x + y = 5
B. –2x + y = 7
C. –2x + y = 11
D. 2x + y = 11
Write y – 3 = 2(x + 4) in standard form.
Write an Equation in Slope-Intercept Form
Distributive Property
Original equation
Add 5 to each side.
Simplify.
Write an Equation in Slope-Intercept Form
Answer: The slope-intercept form of the equation is
A. A
B. B
C. C
D. D
A B C D
0% 0%0%0%
Write 3x + 2y = 6 in slope-intercept form.
A.
B. y = –3x + 6
C. y = –3x + 3
D. y = 2x + 3
Write the point-slope form of the lines containing the bases of the trapezoid.
Write an Equation in Point-Slope Form
A. GEOMETRY The figure shows trapezoid ABCD with bases AB and CD.
Write an Equation in Point-Slope Form
Step 1 First find the slopes of AB and CD.
(x1, y1) = (–2, 3)
(x2, y2) = (4, 3)
Slope formula
Slope formula
(x1, y1) = (1, –2)
(x2, y2) = (6, –2)
AB:
CD:
Step 2 You can use either point for (x1, y1) in the point-slope form.
Write an Equation in Point-Slope Form
Method 1 Use (–2, 3).AB: Method 2 Use (4, 3).AB:
y – y1 = m(x – x1)
y – 3 = 0(x + 2)
y – 3 = 0
y – y1 = m(x – x1)
y – 3 = 0(x – 4)
y – 3 = 0
Write an Equation in Point-Slope Form
Answer: The point-slope form of the equation containing AB is y – 3 = 0. The point-slope form of the equation containing CD is y + 2 = 0.
CD: Method 1 Use (1, –2). CD: Method 2 Use (6, –2).
y – y1 = m(x – x1)
y + 2 = 0(x – 1)
y + 2 = 0
y – y1 = m(x – x1)
y + 2 = 0(x – 6)
y + 2 = 0
B. Write each equation in standard form.
Answer: y = –2
Write an Equation in Point-Slope Form
Answer: y = 3
Original equation
Add 3 to each side.
Simplify.
Original equation
Subtract 2 from each side
Simplify.
AB: y – 3 = 0
y – 3 + 3 = 0 + 3
CD: y + 2 = 0
y + 2 – 2 = 0 – 2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. y – 6 = 1(x – 4)
B. y – 1 = 1(x – 3)
C. y + 4 = 1(x + 6)
D. y – 4 = 1(x – 6)
A. The figure shows right triangle ABC. Write the point-slope form of the line containing the hypotenuse AB.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. –x + y = 10
B. –x + y = 3
C. –x + y = –2
D. x – y = 2
B. The figure shows right triangle ABC. Write the equation in standard form of the line containing the hypotenuse.
Five-Minute Check (over Lesson 4-5)
Main Ideas and Vocabulary
Targeted TEKS
Key Concept: Scatter Plots
Example 1: Analyze Scatter Plots
Example 2: Find a Line of Fit
Example 3: Linear Interpolation
• scatter plot
• positive correlation• negative correlation• line of fit• best-fit line• linear interpolation
• Interpret points on a scatter plot.
• Use lines of fit to make and evaluate predictions.
TECHNOLOGY Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe it.
Answer: The graph shows a negative correlation. With each year, more computers are in Maria’s school, making the students-per-computer rate smaller.
Analyze Scatter Plots
The graph shows the average students per computer in Maria’s school.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. Positive correlation; with each year, the number of mail-order prescriptions has increased.
B. Negative correlaton; with each year, the number of mail-order prescriptions has decreased.
C. No correlation
D. Cannot be determined
Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe it.
The graph shows the number of mail-order prescriptions.
POPULATION The table shows the world population growing at a rapid rate.
Find a Line of Fit
Interactive Lab:Analyzing Linear Equations
A. Draw a scatter plot and determine what relationship exists, if any, in the data.
Let the independent variable x be the year and let the dependent variable y be the population (in millions).
The scatter plot seems to indicate that as the year increases, the population increases. There is a positive correlation between the two variables.
Find a Line of Fit
B. Draw a line of fit for the scatter plot.
No one line will pass through all of the data points. Draw a line that passes close to the points. A line is shown in the scatter plot.
Find a Line of Fit
C. Write the slope-intercept form of an equation for equation for the line of fit.
The line of fit shown passes through the data points (1850, 1000) and (2004, 6400).
Find a Line of Fit
Step 1 Find the slope.
Slope formula
Let (x1, y1) = (1850, 1000) and (x2, y2) = (2004, 6400)
Simplify.
Step 2 Use m = 35.1 and either the point-slope form or the slope-intercept form to write the equation. You can use either data point. We chose (1850, 1000).
Find a Line of Fit
Point-slope form
y – y1 = m(x – x1)
y – 1000 35.1x – 64,935)
y – 1000 35.1 (x – 1850)
y 35.1x – 63,935
Find a Line of Fit
Slope-intercept form
y = mx + b
1000 64,935 + b
1000 = 35.1 (1850) + b
–63,935 b
y 35.1x – 63,935
Answer: The equation of the line is y 35.1 – 63,935.
1. A
2. B
3. C
4. D
The table shows the number of bachelor’s degrees received since 1988.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. There is a positive correlation between the two variables.
B. There is a negative correlation between the two variables.
C. There is no correlation between the two variables.
D. Cannot be determined
A. Draw a scatter plot and determine what relationship exists, if any, in the data.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. B.
C. D.
B. Draw a line of best fit for the scatter plot.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. y = 8x + 1137
B. y = –8x + 1104
C. y = 6x + 47
D. y = 8x + 1104
C. Write the slope-intercept form of an equation for the line of fit.
Use the prediction equation y 35.1x – 63,935, where x is the year and y is the population (in millions), to predict the world population in 2010.
Answer: 6,616,000,000
Linear Interpolation
y 35.1x – 63,935
y 6616
y 35.1 (2010) – 63,935
Original equation
Simplify.
Replace x with 2010.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 1,204,000
B. 1,104,000
C. 1,104,008
D. 1,264,000
Use the equation y = 8x + 1104, where x is the years since 1998 and y is the number of bachelor’s degrees (in thousands), to predict the number of bachelor’s degrees that will be received in 2015.