An equation whose graph is a line is called a linear equation. Linear equations may contain one or more variables with no variable having an exponent other that 1.

For example:

 Equation Linear? x+3y=6 yes no

Student Activity

Check the box next to each equation if it is linear. If it is not linear, explain why.

1.

2. x-8y=15

3. f(x)=2x-6

4.

5.

6. y=4

A function is linear if it can be defined by f(x) = mx + b, where m and b are real numbers.

f(x) = mx + b is called the slope-intercept form of an equation.

m = slope

b = y-intercept (0, b)

Given 10x - 2y = 20, the slope-intercept form of the equation is y = 5x - 10.

Student Activity

Write an equation in y = mx + b form for the line that satisfies each of the following conditions.

7. 2x - 2y = 4

8. 6y = 3x - 12

9. 5x - y = 10

In the equation y = mx + b, b is the y-intercept (the point where the line crosses the y-axis).

 y = 2x + 5 b = (0, 5)

Finding the y-intercept

Sometimes it is necessary to determine the y-intercept from other information about the line.

For example:

Line 1 : m = and passes through (6, 4). Using y = mx + b:

4 = (6) + b

b = 1

so the equation for Line 1 would be y = x + 1.

Line 2 : passes through (6, 1) and (8, -4).

Using the point (6, 1) and y = mx + b,

1 = (6) + b

b = 16

so the equation for Line 2 would be y = x + b.

Remember: Parallel lines have the same slope and perpendicular lines hav slopes that are opposite reciprocals.

Line 3 : passes through (-2, 0) and is perpendicular to the line y = -3x + 7

0 = (-2) + b

b =

so the equation for Line 3 would be y = x + .

Student Activity

Write an equaiton in y = mx + b form for each line that satifies the given conditions.

10. Line A

-5y = 3x - 30

11. Line B

and passes through (2, -3)

12. Line C

passes through (-1, -1) and (8, -1)

13. Line D

passes through (4, 2) and is parallel to y = 2x - 4

14. Line E

x-intercept = -3 and the y-intercept = 6

Evaluate the graph below. Write an equation for each of the lines shown below.

15.

16.

17.

18.

19.