Question

What is the slope of any line that is perpendicular to the line 4x - 8y = 64 and why?

a) Slope is 2 because it's the reciprocal of the original line's slope.
b) Slope is -2 because it's the negative reciprocal of the original line's slope.
c) Slope is 4 because it's the double of the original line's slope.
d) Slope is -4 because it's the negative double of the original line's slope.

Answer 1

The slope of a line perpendicular to the line 4x - 8y = 64 is -2, because it is the negative reciprocal of the original line's slope, which is 1/2.

Step-by-step explanation:

To determine the slope of a line that is perpendicular to the given line 4x - 8y = 64, we first need to find the slope of the original line. We can rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope and b the y-intercept. By rearranging the equation, we get 8y = 4x - 64, and then y = (1/2)x - 8. The slope of the original line is therefore 1/2. A line that is perpendicular to this one will have a slope that is the negative reciprocal of 1/2, which is -2.

Therefore, the correct answer is: b. Slope is -2 because it's the negative reciprocal of the original line's slope.