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.


Fill in your name below and print a copy of your answers.

 

Name


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