Question

What is the linear equation of a line that goes through (-8, 4) and (6, -3)?

A) y = 2x
B) y = 0.5x
C) y = -2x
D) y = -0.5x

Answer 1

To find the linear equation of a line through the points (-8, 4) and (6, -3), calculate the slope (m = -0.5) and use the point-slope form to write the equation as y = -0.5x, which is option D).

Step-by-step explanation:

The linear equation of a line that passes through the points (-8, 4) and (6, -3) can be found using the slope formula, which is (y2 - y1) / (x2 - x1), and the point-slope form of a linear equation, which is y - y1 = m(x - x1).

First, calculate the slope (m):
m = (-3 - 4) / (6 - (-8))
m = (-7) / (14)
m = -1/2 = -0.5

Then, use one of the points and the slope to write the equation. Using the point (-8, 4):
y - 4 = -0.5(x + 8)
y - 4 = -0.5x - 4
y = -0.5x

So the equation of the line is y = -0.5x, which corresponds to answer option D).