Which of the following are point-slope equations of the line going through (9,3) and (-3,-6)? Check all that apply.

Question

y - 3 = 4/3 (x - 9)
y + 6 =3/4  (x + 3)
y - 3 = 3/4 (x - 9)
y - 6 = 4/3 (x - 3)
y - 6 = 3/4 (x - 3)
y + 6 =4/3  (x + 3)

Answer 1

Hi again Alina;

Let's first establish slope.

Slope is change-of-y divided by change-of-x...

m=(y-y₁)/(x-x₁)

(9,3) and (-3,-6)

m=(3--6)/(9--3)

Subtracting a negative number is the same as adding a positive number...

m=(3+6)/(9+3)

m=9/12

Both the 9 and 12 are divisible by 3...

9/3=3

12/3=4

m=3/4

Point-slope formula is...

y-y₁=m(x-x₁)

We will use either point.  Let's begin with the first, (9,3)...

y-3=(3/4)(x-9)

THIS IS THE THIRD ANSWER...y - 3 = 3/4 (x - 9)

 

Second point, (-3,-6)...

y-y₁=m(x-x₁)

y--6=(3/4)(x--3)

y+6=(3/4)(x+3)

THIS IS THE SECOND ANSWER...y + 6 =3/4 (x + 3)