Using a Point & Slope to find the Equation

What we are doing today….

We are going to learn how to take a point and a slope and turn it into y = mx + b.

For example: (3, 5) and m = 2 will become y = 2x - 1

Finding an equation • When given a point and a slope– For example, find the equation of a line with the

point (2, 8) and a slope of 3• First, use the slope-intercept equation y=mx+b• Look at the information you are given

(2, 8) and a slope of 3

• Plug these into y = mx + b• Our new problem looks like 8= 3(2) + b• Let’s simplify 8 = 6 + b

-6 -6 2 = b

x y m

• We now know the slope and y-intercept m = 3 b = (0, 2) Let’s plug into y = mx + b y = 3x + 2

Finding an equation • When given a point and a slope– For example, find the equation of a line with the

point (-2, 3) and a slope of -4• First, use the slope-intercept equation y=mx+b• Look at the information you are given

(-2, 3) and a slope of -4

• Plug these into y = mx + b• Our new problem looks like 3= -4(-2) + b• Let’s simplify 3 = 8 + b

-8 -8 -5 = b

x y m

• We now know the slope and y-intercept m = -5 b = (0, -4) Let’s plug into y = mx + b y = -5x – 4

Finding an equation • When given a point and a slope– For example, find the equation of a line with the

point (-8, -6) and a slope of 1/2 • First, use the slope-intercept equation y=mx+b• Look at the information you are given

(-8, -6) and a slope of 1/2

• Plug these into y = mx + b• Our new problem looks like -6= 1/2(-8) + b• Let’s simplify -6 = -4 + b

+4 +4 -2 = b

x y m

• We now know the slope and y-intercept m = 1/2 b = (0, -2) Let’s plug into y = mx + b y = 1/2x – 2

Finding an equation • You try these problemsA) (1, 8) m = 4

B) (-3, -5) m = 1/3

C) (0, 5) m = -2

D) (6, 2) m = 0

y = 4x + 4

y = x – 2

y = -2x + 5

y = 2

Practice• Write a linear equation using the point and the slope for the

following. Then graph the line.

1. (1,1) and m =1/4 2. (6,0) and m = -1/2

3. (-2,1) and m = 1 4. (-6,-2) and m = -1/3

5. (3,-4) and m = 0 6. (-4,1) and m = 3/2

7. (0,0) and m = -3 8. (5,-3) and m = none/ undefined