Question

Which equation represents a line that is perpendicular to the line passing through (-4,7) and (1,3)?

a. y = -5/4x - 2
b. y = 5/4x + 8
c. y = -4/5x + 6
d. y = 4/5x - 3

Answer 1

The equation representing a line perpendicular to the one passing through (-4,7) and (1,3), with its slope being -4/5, is y = 5/4x + 8.

Step-by-step explanation:

To find the equation of a line that is perpendicular to another, we need to determine the slope of the original line and then find the negative reciprocal of that slope. The slope between the points (-4,7) and (1,3) can be found using the formula (y2-y1)/(x2-x1). The slope is (3-7)/(1+4) = -4/5. A line perpendicular to this one will have a slope of the reciprocal, which is 5/4. Thus, the equation must have a slope of 5/4 or -5/4. Now we can eliminate options that don't have the correct slope. Option (a) y = -5/4x - 2 has the correct slope but with a negative sign, which would make it parallel, not perpendicular. Option (b) y = 5/4x + 8 has the correct slope of 5/4 and is thus the perpendicular line we are looking for.