3.6 Finding the Equation of a Line

Slope-Intercept Form

What are the two things needed to write the equation of a line in slope-intercept form?

1.

2.

Slope

y-intercept

Write an Equation Given a Slope and a Point on the Line

Example: Set up your equation by substituting in

the slope.

What can you do to find the y-intercept? Find the y-intercept!

What is the equation of the line?

3;5,2 mP

bxy 3

b 235

113 xy

Determine an equation in the form

of the line passing through the given point

P with the given slope m.

1.

2.

bmxy

2;0,5 mP

3

2;1,4 mP

Write an Equation Given 2 Points on the Line:

Example: Find the slope!

Set up your equation by substituting in the slope.

What can you do to find the y-intercept? Find the y-intercept!

What is the equation of the line?

9,8,3,6 68

39

m

bxy 3

b 633

153 xy

Determine an equation in the form of the line containing the two given points.

3.

4.

bmxy

2

9,1,3,4

2,8,2,5

Parallel Lines In your graphing calculator, graph the

following:

What do you notice about all three graphs?

What is the same about each equation? What is different about each equation? So, to sum it up lines

have the slope!

32

11 xY 2

2

12 xY 5

2

13 xY

parallel

same

Determine the equation in the form of the line through the given point satisfying the given equation.

5. ; parallel to

6. ; parallel to the line containing

and

8,6 13

2 xy

12,3 0,6 5,4

Perpendicular Lines

Perpendicular lines on the other hand have

slopes!

opposite

reciprocal

Find the slope of a line perpendicular to the given line.

7.

8.

9.

92

1 xy

937 yx

2y

Determine the equation in the form of the line through the given point satisfying the given equation.

10. perpendicular to

11. Perpendicular to the line through

and

10,3 43 xy

2,6

1,

3

2

7,

3

4