GRAPHING LINES
GRAPHING LINES. I N THIS SECTION : You will learn to graph ordered pairs You will learn to graph linear equations in two variables You will learn the.
Mar 26, 2015
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
GRAPHING LINES
IN THIS SECTION: You will learn to graph ordered pairs
You will learn to graph linear equations in two variables
You will learn the standard form of a line.
You will learn to graph a line by using the x and y intercepts.
You will verify whether a point lies on a line.
COORDINATE SYSTEM: (X,Y)
1 2 3 4 5 6 7-1-2-3-4-5-6-7
1
2
3
4
5
6
7
-1
-2
-3
-4
-5
-6
-7
x
y
Quadrant I (x,y)
Quadrant II (- x,y)
Quadrant III (- x,- y)
Quadrant IV (x,- y)
Origin(0,0)
A (2,3)
B (-3, 1)
C (-3, -5)
D (2, -6)
PLOTTING POINTS: (X,Y)
1 2 3 4 5 6 7-1-2-3-4-5-6-7
1
2
3
4
5
6
7
-1
-2
-3
-4
-5
-6
-7
x
y
E (0,3)
D (0,-3)
F (3,0)
G (-3,0)
PLOTTING POINTS: (X,Y)
1 2 3 4 5 6 7-1-2-3-4-5-6-7
1
2
3
4
5
6
7
-1
-2
-3
-4
-5
-6
-7
x
y
1) (0,4)2) (-4,3)3) (-4,-5)4) (4,-5)5) (4,3)6) (0,4)Lift your pencil
GRAPH DESIGNS: WHAT DO THESE POINTS MAKE?
1 2 3 4 5 6 7-1-2-3-4-5-6-7
1
2
3
4
5
6
7
-1
-2
-3
-4
-5
-6
-7
x
y
STANDARD FORM OF A LINE:
Linear Equations can be written in standard
form : Ax By C
Examples of equations in standard form :
) 3 4 3 ) 5 2 9a x y b x y
Examples of equations in standard form :
3) 3 4 3 ) 1
n t
4
o
a x y b y x
LINEAR GRAPHS:Do these points lie on the same line?
1 2 3 4 5 6 7-1-2-3-4-5-6-7
1
2
3
4
5
6
7
-1
-2
-3
-4
-5
-6
-7
x
y
A 5,2
B 4, 0
C 3, 2
D 1, 4
LINEAR GRAPHS:Do these points lie on the same line?
1 2 3 4 5 6 7-1-2-3-4-5-6-7
1
2
3
4
5
6
7
-1
-2
-3
-4
-5
-6
-7
x
y
A 5, 6
B 2, 4
C 1, 2
D 7, 2
LINEAR GRAPHS:Can you identify three points that lie on
this line?
1 2 3 4 5 6 7-1-2-3-4-5-6-7
1
2
3
4
5
6
7
-1
-2
-3
-4
-5
-6
-7
x
y
LINEAR GRAPHS:Can you identify three points that lie on
this line?
1 2 3 4 5 6 7-1-2-3-4-5-6-7
1
2
3
4
5
6
7
-1
-2
-3
-4
-5
-6
-7
x
y
VERIFYING A POINT ON A LINE:
If you want to verify whether a point lies on the line, then you just need to plug in the values and test whether the equations works out:
Therefore, (2,1) does not lie on this line.
Does 2,1 lie on the line 3 4 7?x y
3 2 4 1 7
6 4 7
10 7
VERIFYING A POINT ON A LINE:
1) Does 2,3 lie on the line 5 7?x y
2) Does 0, 5 lie on the line 3 5?y x
5 2 3 7
10 3 7
13 7
3 5
5 3 0 5
5 5
y x
FINDING THE X AND Y INTERCEPT:
The x-intercept is the point where the line crosses the x-axis.
The y-intercept is the point where the line crosses the y-axis.
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
x
y
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
x
y
FINDING THE X AND Y INTERCEPT:
1) 2)
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
x
y
: 2,0 : 0,2x y : 2,0 : 0, 3x y
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
x
y
FINDING THE X AND Y INTERCEPT:
3) 4)
Do you notice a pattern with the x and y intercepts?
: 3,0 : 0,2x y : 1,0 : 0, 3x y
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
x
y
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
x
y
FINDING THE X AND Y INTERCEPT:
5) 6)
Do you notice a pattern with the x and y intercepts of horizontal and vertical lines?
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
x
y
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
x
y
: 2,0 : nonex y : none : 0,3x y
FINDING THE X AND Y INTERCEPT AND GRAPH:1) x-intercept: you set y = 0 and solve
for x.
2) y-intercept: you set x = 0 and solve for y.
5 2 10x y
5 2 10x y
5 2 0 10x 5 10x
2 2,0x
5 0 2 10y 2 10y
5 0,5y
1) Find the and intercepts of 3 4 12.x y x y
int .: 3 4 0 12
3 12
4
x x
x
x
int .: 3 0 4 12
4 12
3
y y
y
y
1 2-1-2-3-4-5
1
2
3
4
-1
-2
-3
-4
x
y
2) Find the and intercepts of 4 3 8.x y x y
int .: 4 3 0 8
4 8
2
x x
x
x
int .: 4 0 3 8
3 8
8 22
3 3
y y
y
y
1 2 3-1-2-3-4-5
1
2
3
4
-1
-2
-3
-4
x
y
CST PREP PROBLEMS:
1) Which point lies on the graph of 3 4 12.x y
A. 0,4 B. 0, 4
C. 0,3 D. 0, 3
CST PREP PROBLEMS:
2) Which point does lie on the graph of
2 6?
not
x y
A. 0,3 B. 2,2
C. 1,5 D. 4,1
Related Documents
