Which of the following are point-slope equations of the line going through (3, 6) and (1, -2)? Check all that apply.

Question

y + 2 = 4(x - 1)
y - 6 = 1/4 (x - 3)
y - 2 = 1/4 (x - 1)
y - 2 = 4(x + 1)
y - 6 =1/4  (x + 3)
y + 2 = 4(x - 1)

Answer 1

Hi again Alina;

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

m=(y-y₁)/(x-x₁)

(3, 6) and (1, -2)

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

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

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

m=8/2=4

 

Point-slope formula is...

y-y₁=m(x-x₁)

Let's begin with the first set of coordinates, (3, 6)...

y-6=4(x-3)

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

 

Second set of coordinates, (1, -2)...

y--2=4(x-1)

y+2=4(x-1)

THIS IS THE FIRST ANSWER...y + 2 = 4(x - 1)

Answer 2

Hi Lauren;

We first must establish slope.  This is defined as change-of-y divided by change-of-x...

m=(y-y₁)/(x-x₁)

(3, 6) and (1, -2)

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

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

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

m=8/2=4

Point-slope formula is...

y-y₁=m(x-x₁)

We will begin with the first point,  (3, 6)...

y-6=4(x-3)

PLEASE RE-CHECK LIST OF POSSIBLE ANSWERS.

 

Second point, (1, -2)...

y--2=4(x-1)

y+2=4(x-1)

THIS IS THE FIRST ANSWER...y + 2 = 4(x - 1)