Final answer:
After calculating the slope as -3/4 and using one of the points to determine the y-intercept as 2, we find that the line's equation is y = (-3/4)x + 2. This does not match any of the options provided; therefore, the options given by the student seem to be incorrect.
Step-by-step explanation:
To find the equation of a line that passes through the points (-4,-1) and (4,-7), we need to calculate the slope and use one of the points to find the y-intercept of the equation in the slope-intercept form, which is y = mx + b.
First, let's calculate the slope using the formula m = (y2 - y1) / (x2 - x1):
m = (-7 - (-1)) / (4 - (-4)) = (-7 + 1) / (4 + 4) = -6 / 8 = -3 / 4.
Now that we have the slope, we can choose one of the points, for example (-4,-1), and plug it into the slope-intercept formula to find the y-intercept (b).
-1 = (-3/4)(-4) + b
b = -1 - (-3) = -1 + 3 = 2
Now we can write the equation of the line as y = mx + b, which gives us:
y = (-3/4)x + 2.
However, the student's options for answers are all in the form y = mx + b, with m and b being integers. None of the options provided match the equation we have calculated, so it seems there might be an error in the student's options or the calculation. Therefore, all the provided options are incorrect, and the student should re-evaluate the slope calculation or the options provided for accuracy.