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2. Graphing Linear Equations
3.2
Graphing Linear Equations

3. 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.

4. 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.

5. 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.

6. 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.

7. Example (cont) Graph the linear equation 2x – y = – 4.
Next, let x = – 3.
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).

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

9. 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).

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

11. 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).

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

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

14. 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.

15. Graphing Linear Equations
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