What is an equation of the line that passes through the points ( − 6 , 2 ) (−6,2) and ( − 4 , − 1 ) (−4,−1)? Put your answer in fully reduced form.

Answer 1

(-6,2) and (-4,-1) are the 2 points.

x1=-6

y1=2

x2=-4

y2=-1

First find the slope (m) which can be found with: m=(y2-y1)/(x2-x1)

So m=(-1-2)/(-4- -6) = -3/2

m=-3/2

Now, using this formula: y-y1=m(x-x1)

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

Now simplify by distributing (-3/2) and then adding -2 to the right side:

y=(-3/2x-9)+2

y=-3/2x-7

Answer 2

First determine the slope between (-6,2) and (-4,-1) = (-1-2)/(-4--6) = -3/2

in point slope form: y - y1 = m(x-x1) where (x1,y1) = one of the points, say (-4,-1):

y + 1 = -3/2 (x + 4)

to get into slope intercept form: y = mx + b

multiply both sides by 2:

2y + 2 = -3(x+ 4)

expand right side

2y + 2 = -3x - 12

solve for y

2y = -3x - 14

y = -3/2x - 7

move x term to left side to get into general form: ax + by = c

3/2x + y = -7