A line in the xy-plane passes through the points (1,-2) And has a slope of 1/3. Which of the following points lies on the line? A) (3,-2)
B) (2,-4/3)
C) (0,-2)
D) (-1,-8/3)

D) (-1,-8/3)

Explanation:

To solve this we need the point-slope formula, because we are given a point and a slope.

y-y₁=m(x-x₁)

In this problem, m=1/3 and (x₁, y₁)=(1, -2)

So when we plug these into the formula we have

y- -2 = 1/3(x-1)  (I will rewrite y - -2 as y+2 because subtracting a negative is the same as adding a positive).

Now we can plug each of the points from the multiple choice into the equation. If one of them works (gives us a true statement), that's our answer.

A) use 3 for x and -2 for y.

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

0 = 1/3 (2)

0=  2/3 This is not correct, so A is not the answer.

B) use 2 for x and -4/3 for y

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

2/3 = 1/3 (1)

2/3 = 1/3 This is not correct, so B is not the answer.

C) Use 0 for x and -2 for y.

-2+2 = 1/3(0-1)

0=1/3(-1)

0=-1/3 This is not correct, so C is not the answer

D) Use -1 for x and -8/3 for y.

-8/3 +2=1/3(-1-1)

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

-2/3 = -2/3 This is a true statement. Plus, we had already eliminated A, B, and C, so it would have to be D if our calculations were correct.