Question

Which equations are equations for the line shown?

Answer 1

From point (-3, 1) to point (3, 4) you go up 3 and right 6.
Slope = rise/run = 3/6 = 1/2

All choices are equations written in the point-slope form,

$y - y_1 = m(x - x_1)$

The first choice shows a slope of -1/2, so the first choice is incorrect.

If you use that form the equation of a line with the correct slope, m = 1/2,
and point (-3, 1), you get

$y - 1 = \dfrac{1}{2}(x + 3)$

This is choice D, so choice D is correct.

If you use that form the equation of a line with the correct slope, m = 1/2,
and point (3, 4), you get

$y - 4 = \dfrac{1}{2}(x - 3)$

This is choice B, so choice B is correct.

Now we need to look at choice C.

$y - y_1 = \dfrac{1}{2}(x - x_1)$

$y - 3 = \dfrac{1}{2}(x + 1)$

$y - 3 = \dfrac{1}{2}(x - (-1))$

Choice C uses the correct slope 1/2, but it uses point (-1, 3).
From the graph, we see that point (-1, 3) is not part of the graph of the equation, so choice C is incorrect.

Answer: B, D