Question

Which of the following points would fall on the line produced by the point-slope form equation y + 12 = 3(x - 4) when graphed?

(1, 21)
(2, 18)
(3, -15)
(-1, 21)

Answer 1

(3, -15)

Explanation:

We can solve for the y-coordinate of each point using the given equation and then check if it satisfies the equation for the corresponding x-coordinate.

For point (1, 21):

y + 12 = 3(x - 4)

y + 12 = 3(1 - 4)

y + 12 = -9

y = -21

(1, 21) does not fall on the line.

For point (2, 18):

y + 12 = 3(x - 4)

y + 12 = 3(2 - 4)

y + 12 = -6

y = -18

(2, 18) does not fall on the line.

For point (3, -15):

y + 12 = 3(x - 4)

-15 + 12 = 3(3 - 4)

-3 = -3

(3, -15) falls on the line.

For point (-1, 21):

y + 12 = 3(x - 4)

y + 12 = 3(-1 - 4)

y + 12 = -15

y = -27

(-1, 21) does not fall on the line.

Therefore, only point (3, -15) falls on the line.