Chapter 7 Section 2 Graphing Linear Equations
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Chapter 7 Section 2
Graphing Linear Equations
Learning Objective
Graph linear equation by plotting points.
Graph linear equation in the form of ax + by = 0
Graph linear equations using the x- and y-intercepts.
Graph horizontal and vertical lines.
Study applications of graphs.
Key Vocabulary: linear equation in two variables, graph of an equation, x-intercept, y-intercept, horizontal line, vertical line.
Graphing Linear Equations
There are two methods that can be used to graph linear equations. Graph by plotting points Graph by the x-intercept (x, 0) and y-intercept (0, y)
Graph by plotting points Solve for y. (get y by itself on the left side of the equal sign) Select a value for x. substitute the value in the equation and find y.
Record the ordered pair (x,y) Repeat for 2 more ordered pairs. Plot the pairs, they should be collinear. Draw a straight line, with arrow on both ends) through the three points
The scale of your axes will result in a different look.
Graph Linear Equations by Plotting Points
Example:
y = 2x + 1
x y
0 1
1 3
2 5
y = 2x + 1
y = 2(0) + 1
y = 1
y = 2x + 1
y = 2(1) + 1
y = 3
y = 2x + 1
y = 2(2) + 1
y = 5
(0,1)
(1,3)
(2,5)
(0,0) x
y
Graph Linear Equations by Plotting Points
Example:
2y = 3x – 4
x y
0 -2
2 1
4 4
2 3 4
3 4
2
y x
xy
3 4
2(3)0 4 4
2 22
xy
y
y
3 4
2(3)2 4 2
2 21
xy
y
y
3 4
2(3)4 4 8
2 24
xy
y
y
(2,1)
(0,-2)
(4,4)
(0,0) x
y
Graph Linear Equations in the form of ax + by = 0, always passes through the origin
Example:
2x + 3y = 0
x y
0 0
3 -2
6 -4
2 3 0
3 2
2
3
x y
y x
y x
2
32
(0)3
0
y x
y
y
2
32
(3)32
y x
y
y
2
3
2
3
y
y
( 6
2
)
4y
Choose values of x that are multipliers of 3 and the denominator will divide out.
(3,-2)
(0,0)
(6,-4)
xy
Graph Linear Equations using the x- and y-intercept
x-intercept, point at which the graph crosses the x axis
(x, 0)
y-intercept, point at which the graph crosses the y axes
(0, y)
xy-intercept , point at which the line crosses at the origin (0,0)
(0,2) y-intercept
(-2,0) x-intercept
(0,0)
y
x
Graph Linear Equations using the x- and y-intercept
Find y-intercept (0, y) by setting x = 0 and find the value for y.
Find the x-intercept (x, 0) by setting y = 0 and find the value for x.
Find a checkpoint by selecting a non-zero number for x and find y.
Plot y-intercept, x-intercept and the checkpoint, should be collinear (a straight line)
Draw line with arrows on each end.
Graph Linear Equations using the x- and y-intercept
Example:
4y = 8x + 4
x y
0 1
-1/2 0
1 3
4 8 4
8 4 8
4
y x
xy
2
4
x 4
4
2 1y x
2 1
2(0) 1
1
y x
y
y
2 1
0 2 1
1 2
1
2
y x
x
x
x
2 1
2(1) 1
3
y x
y
y
(0,1)
(1,3)
(-1/2,0)(0,0) x
y
Graph Linear Equations using the x- and y-intercept
Example:
3x + 5y = 9
x y
0 9/5
3 0
1 4/3
6 -7
-3 8
3 5 9
5 9 3
3 9
5
x y
y x
xy
3 9
53(0) 9
59 4
15 5
xy
y
y
5 9
35(0) 9 9
3 33
yx
x
x
(0,3)
(1,4/3)(9/5,0)
3 5 9
3 9 5
5 9
3
x y
x y
yx
5 9
35(1) 9 4 1
13 3 3
xx
x
(0,0) x
y
Graph Linear Equations using the x- and y-intercept
Example:
y = 10 x + 20
x y
0 20
-2 0
1 30
10 20
10(0) 20
20
y x
y
y
10 20
20 10
20
10
y x
y x
yx
(0,20)
(-2,0)
10(1) 20
10 20
30
y
y
y
(1,30)
(0,0) x
y
20
100 20
102
yx
x
x
Graph Horizontal Lines
The graph of an equation of the form y = b is a horizontal line, whose y-intercept is (0,b)
Example:
y = -2
(0,-2)
Means x = 0(0,-2)
(0,0) x
y
Graph Vertical Lines
The graph of an equation of the form x = a is a vertical line, whose x-intercept is (a,0)
Example:
x = 4
(4, 0)
Means y = 0
(4,0)(0,0) x
y
Remember
It is not necessary to always solve for y first. However, it can be helpful in finding values for x.
Pick values that are easy to work with, such as 0 and 1 when possible.
Try to pick values that will divide out a fraction when possible.
Every point on a graph represents an ordered pair solution to the equation of the graph.
HOMEWORK 7.2
Page 439:
#21, 23, 25, 29, 35, 45, 47, 50, 61, 65, 67
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