Question

Line m passes through the points (-2,7) and (4,-5), as shown below. Which of the following could be the equation of a line that is parallel to line m?

Answer 1

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be parallel, they need to have the same slope.

To find the slope (m), use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$      And plug in the two points

(-2, 7) = (x₁, y₁)

(4, -5) = (x₂, y₂)

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-5-7}{4-(-2)}$   (two negative signs cancel each other out and become positive)

$m=\frac{-5-7}{4+2}$

$m=\frac{-12}{6}$     Simplify the fraction

m = -2        

The slope is -2, so the parallel line's slope is also -2.

Your answer is C