You will be able to:

Write an equation of a line given one point and slope

Write Equations given Point and Slope: 1. __________________________________ 2. __________________________________

3.___________________________________

4.___________________________________

Make a b/m/x/y chart

Plug in m, x, and y

Solve for b

Rewrite equation in y = mx+b

1. Find the equation of the line through the point (1, -3) and has a slope of -4.

1. Find the equation of the line through the point (1, -3) and has a slope of -4.

bmxy

-4

1-3

(x,y)

y = mx + b-3 =

+4 +41 = b

(0, 1)(-4)(1)+ b

-3 =-4 + b

y = -4x + 1

y = -4x + 1

y = -4x + 1 +4x +4x4x + y = 1

4x + y = 1

2. Write an equation of the line that passes through the point (4, 2) with a slope of 3.

bmxy

3

42

(x,y)

y = mx + b2 =

-12 -12-10 = b

(0, -10)(3)(4)+ b

2 = 12 + b

y = 3x – 10

y = 3x – 10

y = 3x – 10-3x -3x-3x + y = – 10–1 –1 –1

3x – y = 10 3x – y = 10

3. Write an equation of the line that passes through the point (-2, -5) with a slope of ½.

bmxy

1/2

-2-5

(x,y)

y = mx + b-5 =

+1 +1-4 = b

(0, -4)(½)(-2)+ b

-5 = -1 + b

y = ½x – 4

y = ½x – 4

y = ½x – 4

-x -x

-x + 2y = – 8–1 –1 –1

x – 2y = 8 x – 2y = 8

(2) (2) (2)

2y = x – 8

4. Write an equation of the line that passes through the point (5, -4) with a slope of 3/5.

bmxy

3/5

5-4

(x,y)

y = mx + b-4 =

-3 -3-7 = b

(0, -7)(5) + b

-4 = 3 + b

y = x – 7

3

5

3

5

-3x -3x

-3x+ 5y = – 35–1 –1 –1

3x – 5y = 35 3x – 5y = 35

(5) (5) (5)

5y = 3x – 35

y = x – 73

5

y = x – 73

5

5. Write an equation of the line that passes through the point (-3, 0) with a slope of 5.

bmxy

5

-30

(x,y)

y = mx + b0 =

+15 +1515 = b

(0, 15)(5)(-3) + b

0 = -15+ b

y = 5x + 15

y = 5x + 15

y = 5x + 15-5x -5x-5x + y = 15–1 –1 –1

5x – y = -15 5x – y = -15

6. Write an equation of the line that passes through the point (12, -5) with a slope of -3/4.

bmxy

3/4

12-5

(x,y)

y = mx + b-5 =

+9 +94 = b

(0, 4)(12) + b

-5 = -9 + b

y = x + 4

3

4

3

4

3

+3x +3x

3x + 4y = 16

3x + 4y = 16

(4) (4) (4)

4y = -3x + 16

y = x + 43

4

y = x + 43

4

-9

3

bmxy

-3

7. Find the equation of the line that passes through the two points.

(3, 4)

34

bmxy

-3

34

y = mx + b4 =

+9 +913 = b

(0, 13)(3)+ b

4 = -9 + b

y = x+ 13

(-3)

-3

y = -3x+ 13

y = -3x+ 13+3x +3x3x + y = 13

3x + y = 13

2

3

bmxy

2/3

8. Find the equation of the line that passes through the two points.

(-3, 6)

-36

bmxy

2/3

-36

(0, 8) y = mx + b6 =

+2 +28 = b

(-3) + b

6 = -2 + b

y = x + 8

2

3

2

3

-1

-2x -2x

-2x+ 3y = 24–1 –1 –1

2x – 3y = -24 2x – 3y= -24

(3) (3) (3)

3y = 2x + 24

y = x + 82

3

y = x + 82

3