Choose the equation that represents a line that passes through points (−6, 4) and (2, 0). A x + 2y = 2 B 2x − y = −16 C x + 2y = −8 D 2x + y = 4

Answer 1

I recommend using slope-intercept form here, y = mx + b where m = gradient and b = y intercept.

Gradient is defined as change in y / change in x.

For our 4 choices, I will first rearrange them to fit slope-intercept form:

(A) x + 2y = 2 => 2y = -x + 2 => y = -1/2 x + 1

(B) 2x - y = -16 => y = 2x + 16

(C) x + 2y = -8 => 2y = -x - 8 => y = -1/2 x - 4

(D) 2x + y = 4 => y = -2x + 4

Next, let's work out the gradient between our two points...

m = change in y / change in x

starting at (-6,4) we go down 4 units, and we go across 8 units to get to (2,0).

So m = -4/8 = - 1/2

Which means it's either (A) or (C).

Going from x = -6 to x = 2 the line has crossed the y axis, but the intercept is positive as y went from 4 to 0. (A) has positive intercept, b = 1. Our answer is (A).

Answer 2

Hi, Kevin,

Plug the given data points into each equation to see which one works for both points:

The first equation works for both points. None of the others do.

Bob