Slope intercept equation?

Question

Given points A (0,3) , B (-6,2) , C (-3,6), find the slope-intercept equation of the line that passes through C and is parallel to AB.
I forgot what I'm supposed to do, help please.

Answer 1

Step1 to find the AB line equation.

A(0,3) = (x1,y1)

B(-6,2) = (x2,y2)

Line equation is y-y1 = y2-y1/x2-x1 (x-x1)

y-3 = 2-3/-6-0 (x-0)

y-3 = -1/-6 (x)

y-3 = x/6

y = x/6+3

It is in slope intercept form m1 = 1/6

step2 to find m2

required line slope be the m2.

It is parallel to AB

So m2 = 1/6

step3  to find final line equation

it passes through C(-3, 6)

y-6 = 1/6(x-(-3))

y-6 = 1/6(x+3)

y = x/6+3/6+6

y = x/6 +39/6

The line which is passes through the C and parlell to AB is y = x/6+39/6

Answer 2

Slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

The line is passing through the point C and parallel to line AB.

Parallel lines has same slope. So, first find the slope of the line AB usinf slope formula

m = (y2 - y1) / (x2 - x1)

m = (2 - 3) / (-6 - 0) = -1 / -6 = 1/6

Write the line  equation using the slope. y = 1/6x + b

Next, find the y-intercept value by substituing point C (-3, 6) 

6 = 1/6 * -3 + b ------> b = 6 + 1/2 = 13/2

The line equation is y = 1/6 x + 13/2