Question

Write the equation of the line that passes through the points (-4, -4) and (-2, -8). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

a) y=−2x+6
b) y=−2x−2
c) y=2x−6
d) y=2x+2

Answer 1

The equation of the line that passes through (-4, -4) and (-2, -8) is found by calculating the slope and using the point-slope form to derive y = -2x - 12. However, this equation does not match any of the options provided, suggesting an error in the question or options.

Step-by-step explanation:

To find the equation of the line that passes through the points (-4, -4) and (-2, -8), we first need to calculate its slope (m). The slope is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the given points. Applying this to our points:

m = (-8 - (-4)) / (-2 - (-4)) = (-8 + 4) / (-2 + 4) = -4 / 2 = -2

The slope of the line is -2. Next, we use the point-slope form of a line, y - y1 = m(x - x1), with one of our points and the slope to find the line equation. Let's use the point (-4, -4):

y - (-4) = -2(x - (-4))

y + 4 = -2x - 8

y = -2x - 8 - 4

y = -2x - 12

However, none of the options provided, a) y = -2x + 6, b) y = -2x - 2, c) y = 2x - 6, d) y = 2x + 2, matches this equation. There might be a mistake in the problem or in the options provided. Therefore, based on the information given, none of the answer options listed are correct.