1. 3
Chapter
Chapter 2
Graphing

2. Graphing Linear Equations
Section
3.2
Graphing Linear Equations

3. Identifying Linear Equations
Objective 1
Identifying Linear Equations

4. Linear Equation in Two Variables
Linear Equations
Linear Equation in Two Variables
A linear equation in two variables is an equation that can be written in the form
Ax + By = C
where A, B, and C are real numbers and A and B not both 0. This form is called standard form. The graph of a linear equation in two variables is a straight line.

5. Example
Determine whether each equation is a linear equation in two variables. a. y2 = x + 1 b. y = 7 c.
This is not a linear equation because the y is squared.
This is a linear equation because it can be written 0x + y = 7.
This is a linear equation because is it written in Ax + By = C form.

6. Graphing Linear Equations by Plotting Ordered Pair Solutions
Objective 2
Graphing Linear Equations by Plotting Ordered Pair Solutions

7. Example Graph the linear equation 2x – y = –4.
To graph this equation, we find three ordered pair solutions by choosing a value for one of the variables, x or y, then solving for the other variable. (The third solution acts as a check for the other two.) We plot the solution points, then draw the line containing the 3 points.
Continued

8. Example (cont) Graph the linear equation 2x – y = – 4. Let x = 1.
2(1) – y = –4 Replace x with 1.
2 – y = –4 Simplify.
– y = –6 Subtract 2 from both sides.
y = 6 Multiply both sides by –1.
The ordered pair (1, 6) is a solution of 2x – y = –4.
Continued

9. Example (cont) Graph the linear equation 2x – y = – 4.
Next, let y = 4.
2x – y = –4
2x – 4 = –4 Replace y with 4.
2x = – Add 4 to both sides.
2x = 0 Simplify.
x = 0 Divide both sides by 2.
The ordered pair (0, 4) is a second solution.
Continued

10. Example (cont) Graph the linear equation 2x – y = – 4.
Next, let x = 4.
2x – y = –4
2(–3) – y = –4 Replace x with –3.
–6 – y = –4 Simplify.
–y = 2 Add 6 to both sides.
y = –2 Multiply both sides by –1.
The third solution is (–3, –2).
Continued

11. Example (cont) x y
Now we plot all three of the solutions (1, 6), (0, 4) and (–3, –2).
(1, 6)
(0, 4)
(– 3, – 2)
And then we draw the line that contains the three points.

12. Example
Graph the linear equation –2x + 4y = 8. Find three ordered pair solutions. Let x = 0 –2x + 4y = 8 –2(0) + 4y = y = 8 4y = 8 y = 2 (0, 2)
Let y = 0
–2x + 4y = 8
–2x + 4(0) = 8
–2x + 0 = 8
–2x = 8
x = –4
(–4, 0)

13. Example (cont)
Graph the linear equation –2x + 4y = 8. Find three ordered pair solutions. Let y = 1 –2x + 4y = 8 –2x + 4(1) = 8 –2x + 4 = 8 –2x = 4 x = –2 (–2, 1)
(0, 2), (–4, 0) and (–2, 1)

14. Example Graph the linear equation
Since the equation is solved for y, we should choose values for x.
To avoid fractions, we should select values of x that are multiples of 4 (the denominator of the fraction).
Continued

15. Example (cont) Let x = 4. Graph the linear equation
y = x + 3
y = (4) Replace x with 4.
y = = Simplify.
So one solution is (4, 6).
Continued

16. Example (cont) Graph the linear equation Next, let x = 0. y = x + 3
y = (0) Replace x with 0.
y = = Simplify.
So a second solution is (0, 3).
Continued

17. Example (cont) y = –3 + 3 = 0 Simplify. Graph the linear equation
Next, let x = –4.
y = x + 3
y = (–4) Replace x with – 4.
y = –3 + 3 = Simplify.
So the third solution is (–4, 0).
Continued

18. Example (cont) x y
Now we plot all three of the ordered pair solutions; (4, 6), (0, 3) and (–4, 0).
(4, 6)
(0, 3)
(–4, 0)
And then we draw the line that contains the three points.

19. Helpful Hint
When graphing a linear equation in two variables, if it is
solved for y, it may be easier to find ordered pair solutions by choosing x-values. If it is
solved for x, it may be easier to find ordered pair solutions by choosing y-values.

20. Example Graph the linear equation y = 3.
Can be written in standard form as 0x + y = 3.
No matter what value we replace x with, y is always 3. x y 3 1 5