1. 4.5 Graphing Linear Equations
A linear equation can be written in the form Ax + By = C.
This is called the standard form of a linear equation.
A ≥ 0, A and B are not both zero, and A, B, and C are integers whose greatest common factor is 1.

2. Identify Linear Equations
Determine whether each equation is a linear equation. If so, write the equation in standard form.
y = 5 – 2x
y + 2x = 5 – 2x + 2x
2x + y = 5
The equation is now in standard form where A = 2, B = 1, and C = 5. This is a linear equation.

3. Identify Linear Equations
Determine whether each equation is a linear equation. If so, write the equation in standard form.
b. 2xy – 5y = 6
Since the term 2xy has two variables, the equation cannot be written in the form Ax + By = C. Therefore, this is not a linear equation.

4. Identify Linear Equations
Determine whether each equation is a linear equation. If so, write the equation in standard form.
c. 3x + 9y = 15
Since the GCF of 3, 9, and 15 is not 1, the equation is not written in standard form. Divide each side by the GCF.
3x + 9y = 15
3(x + 3y) = 15
x + 3y = 5
The equation is now in standard form where A = 1, B = 3, and C = 5.

5. Identify Linear Equations
Determine whether each equation is a linear equation. If so, write the equation in standard form.
d. 1/3 y = -1
To write the equation with integer coefficients, multiply each term by 3.
1/3 y = -1
3(1 /3 ) y = 3(-1)
y = -3
The equation y = -3 can be written as 0x + y = -3. Therefore, it is a linear equation in standard form where A = 0, B = 1, and C = -3.

6. Graph Linear Equations
The graph of a linear equation is a line.
The line represents all the solutions of the linear equation.
Also, every ordered pair on this line satisfies the equation.

7. Graph by Making a Table Graph x + 2y = 6.
In order to find values for y more easily, solve the equation for y.
x + 2y = 6
x + 2y – x = 6 – x
2y = 6 – x
y = 3 – ½ x

8. Graph by Making a Table

9. Intercepts
Since two points determine a line, a simple method of graphing a linear equation is to find the points where the graph crosses the x-axis and the y-axis.
The x-coordinate of the point at which it crosses the x-axis is the x-intercept, and the y-coordinate of the point at which the graph crosses the y-axis is called the y-intercept.

10. Graph Using Intercepts
Determine the x-intercept and y-intercept of 3x + 2y = 9. Then graph the equation.
To find the x-intercept, let y = 0.
3x + 2y = 9
3x + 2(0) = 9
3x = 9
x = 3

11. Graph Using Intercepts
Determine the x-intercept and y-intercept of 3x + 2y = 9. Then graph the equation.
To find the y-intercept, let x = 0.
3x + 2y = 9
3(0) + 2y = 9
2y = 9
y = 4.5

12. Graph Using Intercepts
The x-intercept is 3, so the graph intersects the x-axis at (3 , 0). The y-intercept is 4.5, so the graph intersects the y-axis is (0 , 4.5). Plot these points. Then draw a line that connects them.