Algebra

5.3 Writing Linear Equations

Given Two Points

Point Slope Form (PS)

)( 11 xxmyy

Today we will use this formula to find the equation of a line when you are only given two points on the line.

Yesterday you learned to use this formula to find the equation of a line when you were given the slope and one point.

Writing an Equation of a Line from Two Points

STEPS

1. Use the slope formula to find the slope m from the two points

2. Plug one of the points and m into the point slope (PS) formula

3. Simplify to slope-intercept (SI) form

61

6

23

24

m

)3(6)4( xy

•

•

(2, 2)

(3, -4)

Step 1: Compute slope

Step 2: Use PS Form

Step 3: Simplify to SI Form

y + 4 = -6x + 18-4 -4

y = -6x + 14

Check with both points:

Using (3, -4)

2 = -6(2) + 14 -4 = -6(3) + 14

2 = 2 -4 = -4

y = -6x + 14

Now you try. Write the equation of the line through the two given points.

(2, -3) and (-3, 7)

m = -2

PS: y +3 = -2(x – 2) or y – 7 = -2(x + 3)

SI: y = -2x + 1

Write the equation of the line through the two given points.

3

8

)2(3

86)1(

3

82 xyorxy

(-1, -2) and (2, 6)

m =

SI:

PS:

3

2

3

8 xy

Perpendicular Lines

90 90

9090

Perpendicular lines have slopesthat are the opposite of the reciprocal of each other

m = -3

m = 1/3

Write the equation of the line perpendicular to the given line and passing through the given point.

Perpendicular to y = -4x + 6 and passing through (0, 2)

m = ¼

SI: y = ¼x + 2

PS: y – 2 = ¼(x – 0)

Homework

pg. 288 #18-32, 36-41, 45-47, 58-60Graph Paper