Point-Slope Form

Gold Day – 2/26/2015Blue Day – 3/2/2015

Agenda & News

Unit 5 – Linear functions and Applications Standard Form Finding equations of a line using the

intercepts Point-Slope form

Bell Ringer

Find the slope.1. (2, -5) (3, 1)2. (-6, 4) (3, 7)3. (9,0) (0,9)4. (-1,4) (-2,-5)

2 1

2 1

1 2

1 2

Hint: Use either formula

Transforming into Slope intercept form

Change Ax + By=C to y=mx + bEx:1. -3x + 4y = 8 2. 6x + 3y = 27

Transforming into Standard form

Change y=mx + b to Ax + By=C Ex:1. y=x + 2 2. y=- x + 9

Linear Functions

So we have talked about linear functions being represented in a couple of forms. Slope-intercept form▪ Provides an m(slope) & b(y-intercept) for graphing

the line. ▪ We did this on calculator and by hand.

Standard form▪ Can replace the x and y with zeros to find the x-

and y-intercepts for graphing the line Now…point-slope form▪ Provides 1 point and m(slope) to find the graph of

the line.

Point- Slope form is:

)( 11 xxmyy Where m is the slope

and (x1, y1) is the given point

The New Stuff…Point-Slope Form

Point-Slope Form

y – y1 = m(x – x1)

(x1 ,y1) m = rise = slope

point run

Writing in Point-Slope

Given a point and a slope, write an equation in point-slope form

y – y1 = m(x – x1)

Example 1: (3,8) m = 2

y – 8 = 2 (x – 3)

x1, y1

Example 2

y – y1 = m(x – x1)

(-6,1) m = -4

y – 1 = -4(x – (-6))

y – 1 = -4(x + 6)

x1, y1

Quick Check - TPS

y – y1 = m(x – x1)

(5,-2) m= x1, y1

1

2

Example 3 – From 2 Points

Given 2 ordered pairs, write an equation in point-slope form:

(6,3) (-8,5)Steps:1. Find slope

m = y2 – y1

x2 – x1

2. Pick an ordered pair There are 2 possible answers!

Example 6

Given 2 ordered pairs, write an equation in point-slope form:

(-1,-7) (1,3)

Quick Check - TPS

Given 2 ordered pairs, write an equation in point-slope form:

(-4,6) (-2,5)