Question

what is the slope intercept form of
(8,3); m = 5


slope intercept form equation
(-10,-6); m = -5/8

Answer 1

I'll do the hard one, you do the easy one:
(-10,-6); m = -5/8

let y = (-5/8)x + b, sub in (-10,-6)
-6 = (-5/8)(-10) + b
-6 = 25/4 + b
b = -49/4

y = (-5/8)x - 49/4

Answer 2

Slope intercept form equation of straight line:

y = m x + b

where:

m is the slope

b is the y-intercept

In tis case:


1.

( 8 , 3 ) mean x = 8 , y = 3


m = 5

y = 5 x + b

You know coordinates of one point ( 8 , 3 )

Replace x = 8 , y = 3 in equation:

y = 5 x + b

3 = 5 ∙ 8 + b

3 = 40 + b

Subtact 40 to both sides

3 - 40 = 40 + b - 40

- 37 = b

b = - 37

So:

y = 5 x + b

y = 5 x - 37


2.

1.

( -10 , - 6 ) mean x = - 10 , y = - 6


m = - 5 / 8

y = - ( 5 / 8 ) x + b

You know coordinates of one point ( -10 , - 6)

Replace x = -10 , y = - 6 in equation:

y = - ( 5 / 8 ) x + b

- 6 = - ( 5 / 8 ) ∙ ( - 10 ) + b

- 6 = 50 / 8 + b

- 6 = 2 ∙ 25 / 2 ∙ 4 + b

- 6 = 25 / 4 + b

Subtact 25 / 4 to both sides

- 6 - 25 / 4 = 25 / 4 + b - 25 / 4

- 24 / 4 - 25 / 4 = b

- 49 / 4 = b

b = - 49 / 4

So:

y = - ( 5 / 8 ) x + b

y = - ( 5 / 8 ) x - 49 / 4