1. Graphing Linear Equations
Chapter 7 Section 2
Graphing Linear Equations

2. 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.

3. 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)
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.

4. Graph Linear Equations by Plotting Points
Example:
y = 2x + 1
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 x y 1 3 2 5 y
(2,5)
(1,3)
(0,1) x
(0,0)

5. Graph Linear Equations by Plotting Points
Example:
2y = 3x – 4 y
(4,4) x y -2 2 1 4
(2,1) x
(0,0)
(0,-2)

6. Graph Linear Equations in the form of ax + by = 0, always passes through the origin
Example:
2x + 3y = 0 y x
(0,0) x y 3 -2 6 -4
(3,-2)
Choose values of x that are multipliers of 3 and the denominator will divide out.
(6,-4)

7. 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 x
(0,0)
(-2,0) x-intercept

8. 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.

9. Graph Linear Equations using the x- and y-intercept
Example:
4y = 8x + 4 y
(1,3) x y 1
-1/2 3
(0,1)
(-1/2,0) x
(0,0)

10. Graph Linear Equations using the x- and y-intercept
Example:
3x + 5y = 9 y x y
9/5 3 1
4/3 6 -7 -3 8
(9/5,0)
(1,4/3) x
(0,0)
(0,3)

11. Graph Linear Equations using the x- and y-intercept
Example:
y = 10 x + 20 y
(1,30)
(0,20) x y 20 -2 1 30 x
(-2,0)
(0,0)

12. 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 y x
(0,0)
(0,-2)

13. Graph Vertical Lines y x
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 y x
(0,0)
(4,0)

14. 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.

15. HOMEWORK 7.2
Page 439:
#21, 23, 25, 29, 35, 45, 47, 50, 61, 65, 67