Warm-Up1. Find the slope of the line that passes through the two

points:

a. (-2,3) and (5,-1) b. (6,-2) and (-1,-5)

2. Put each equation into slope-intercept form.

a. b.

€

y − 21 =3

5(x +10)

€

y +1 = −2(x − 3)€

m =y2 − y1

x2 − x1

€

m =−1 − 3

5 − −2=

−4

7

€

m =−5 − −2

−1 − 6=

−3

−7=

3

7

€

y − 21 =3

5x + 6

+21 +21

€

y =3

5x + 27

€

y +1 = −2x + 6-1 -1

€

y = −2x + 5

SOLVE FOR “Y”

Warm-Up1. Given slope = -3, and y-intercept = (0,5), create the

equation of the line in slope-intercept form.

2. Look at the graph below and create an equation in slope-intercept form.

€

y = mx +b

y = −3x + 5

m = -1/2

b = (0,2)

€

y = mx +b

y =−1

2x + 2

5.2 Point-Slope Form

What we Know so far….

Slope Intercept Form

bmxy

Where m is the slope and b is the intercept

Write an equation of a line given the slope and the y-intercept.

9intercept = 2

11m y y

7intercept 5

3m y y

21 30,

13 4m

y

9

11x 2

7

3 x 5

21

13x

3

4

y mx b

Write an equation given the slope and y-intercept.

1.

2.

3.

Remember how to graph using slope-intercept form??

Slope-Intercept Form– requires the y-intercept and the slope of the line.

y mx b

m = slope of line b = y-intercept

24

3y x

Slope-Intercept Form:

y mx b

m = slope of line b = y-intercept

62

5y x

What is the equation of this line?

m = -6/5b = (0,2)

Slope-Intercept Form:

y mx b

m = slope of line b = y-intercept

33

2y x

What is the equation of this line?

m = 3/2b = (0,-3)

Slope-Intercept Form:

y mx b

m = slope of line b = y-intercept

34

4y x

What is the equation of the line?

m = 3/4b = (0,4)

What is Point-Slope Form?

€

y − y1 = m(x − x1)

We are going to use this, when given slope, m, and a random point, (x1,y1)

Given a point (1,2) and m = 2/3, write the equation of the line.

€

y − y1 = m(x − x1)

€

y − 2 =2

3(x −1)

What if the directions said to write the equation in slope-intercept form?

€

y − 2 =2

3x −

2

3+2 +2

€

y =2

3x +

4

3

This is the equation of the line in point-slope form!!

Given a point (1,-5) and m = 3, write the equation of the line.

€

y − y1 = m(x − x1)

€

y − (−5) = 3(x −1)

What if the directions said to write the equation in slope-intercept form?

€

y + 5 = 3x − 3

- 5 - 5

€

y = 3x − 8€

y + 5 = 3(x −1) This is the equation of the line in point-slope form!!

Given a point (-3,7) and m = -2, write the equation of the line.

€

y − y1 = m(x − x1)

€

y − 7 = −2(x − (−3))

What if the directions said to write the equation in slope-intercept form?

€

y − 7 = −2x − 6+7 +7

€

y = −2x +1€

y − 7 = −2(x + 3) This is the equation of the line in point-slope form!!

Point-Slope Form – requires the coordinates of a point on the line and the slope of the line. 1 1y y m x x

11 2

3y x

2,11

3m

Point-Slope Form

Point-Slope Form – requires the coordinates of a point on the line and the slope of the line. 1 1y y m x x

32 3

4y x

3,2 3

4m

Point-Slope Form

Point-Slope Form – requires the coordinates of a point on the line and the slope of the line. 1 1y y m x x

44 2

5y x

2, 4 4

5m

13.5 – Equations of Lines

Given a point (2,3) and m = 3 create an equation of the line.

Using Slope-Intercept:

€

y = mx +b

€

3 = 3(2) +b

We don’t know the y-intercept,so let’s plug in what we know and solve for “b”

€

3 = 6 +b-6 -6

€

b = −3Now just plug in the “m” and “b”

€

y = 3x − 3

Using Point-Slope Form:

€

y − y1 = m(x − x1)

Just plug in everything you know!

€

y − 3 = 3(x − 2)Now just solve for “y”

€

y − 3 = 3x − 6

+3 +3

€

y = 3x − 3

Which way is easier???

Using Point-Slope Form

1 2 43

5

-1-2-3-4-5

1

2

3

4

5-1

-2-3

-4

-5

(2,2)

We need the slope and a point:

)2,2(&2

5m

Plug it into the point-slope form

)( 11 xxmyy

)2(2

52 xy

Simplify

€

y − 2 =5

2x − 5

Write the Equation in Point-Slope Form )6,1(

3

1 andm

)( 11 xxmyy

- 6 - 6

€

y =−1

3x +

17

3