1. 9
Graphs and Graphing

2. R.1 Fractions
9.5 Introduction to Graphing Linear Equations
Objectives
Graph linear equations in two variables.
Identify the slope of a line as positive or negative.

3. Graph linear equations in two variables.
Suppose a student taking math and psychology has resolved to spend 6 hours on a weekend studying for the two courses.
Below are possible study combinations.

4. Graph linear equations in two variables.
We can write an equation to represent this study situation.
We list the possible solutions to this equation as ordered pairs. + =

5. Graph linear equations in two variables.
The equation m + p = 6 is called a linear equation. Notice that all the solutions of this equation lie on a straight line.

6. Graph linear equations in two variables.
Plotting the ordered pairs shows a “picture” of the solutions.

7. Graph linear equations in two variables.
Graph x + y = 3. Then use the graph to find a another solution of the equation.
Example
Pick any three values for x and substitute them into the equation to find y.

8. Graph linear equations in two variables.
(continued)
Example
Plot the ordered pairs.
Draw a line through the
points.
Extend the line in both directions.
We see that the point
(–2, 5) is also on the graph.
(0, 3)
(1, 2)
(2, 1)

9. Graph linear equations in two variables.
(continued)
Example
We can check that (–2, 5) is also a solution to the equation by substituting –2 for x and 5 for y.

10. Graph linear equations in two variables.
Graph y = –3x. Then use the graph to find a another solution of the equation.
Example
Pick any three values for x and substitute them into the equation to find y.

11. Graph linear equations in two variables.
(continued)
Example
Plot the ordered pairs.
Draw a line through the
points.
Extend the line in both directions.
We see that the point
(–1, 3) is also on the graph.
(0, 0)
(1, –3)
(2, –6)

12. Graph linear equations in two variables.
(continued)
Example
We can check that (–1, 3) is also a solution to the equation by substituting –1 for x and 3 for y.

13. Identify the slope of a line as positive or negative.
Consider the graph of x + y = 3.
As you move from left to right, the graph slopes downward.
This line has negative slope.

14. Identify the slope of a line as positive or negative.
Consider the graph of
As you move from left to right, the graph slopes upward.
This line has positive slope.

15. Identify the slope of a line as positive or negative.

16. Identify the slope of a line as positive or negative.
Consider the graph of y = –3x. Does the line have positive or negative slope?
Example
The graph of y = –3x has negative slope since it slopes downward as you move from left to right.
As the value of x increases, the value of y decreases.