Question

The point (2,-2) and (-4,13) on the graph of a linear function of x. Which point also lies on the graph of this function?

A. (-6,18)
B. (-1,5)
C. (7,14.5)
D. (13, -4)

Answer 1

A. (-6,18)

Explanation:

The point (2,-2) and (-4,13) on the graph

First we frame an equation of the line using two points

y = mx + b where m is the slope and b is y intercept

slope =
`(y_2-y_2)/(x_2-x_1) =(13+2)/(-4-2) = (15)/(-6) = -2.5`

m = -2.5

Lets find out b

y = mx+b

y= -2.5x + b

Plug in (2,-2) and find out b

-2 = -2.5(2) + b

-2 = -5 + b (add 5 on both sides)

b = 3

so equation of line is y = -2.5 x + 3

Now we check with each option

(-6,18)

Plug in the x and y in our equation and check it

y = -2.5 x + 3

18 = -2.5(-6) + 3

18 = 15+3

18=18 true

So (-6,18) lies on the graph