Final answer:
The value of k is calculated by setting up the slope formula with the slope being the negative reciprocal of the given line's slope, which is 1/5. Option A is correct.
Step-by-step explanation:
To find the value of k if the line through (3, -4) and (-2, k) is perpendicular to y = -5x + 2, we must use the concept of perpendicular lines.
The slope of the given line is -5, and therefore, the slope of the line perpendicular to it will be the negative reciprocal, which is 1/5.
The slope formula is (y2 - y1) / (x2 - x1). We apply the point (3, -4) as (x1, y1) and (-2, k) as (x2, y2). Setting the slope to 1/5, we get:
(k - (-4)) / (-2 - 3) = 1/5
Simplifying:
(k + 4) / -5 = 1/5
Multiplying both sides by -5, we get:
k + 4 = -1
Subtracting 4 from both sides gives us k = -5.
Hence, option A is correct.
Complete question:
Find the value of k if the line through (3, -4) and (-2, k) is perpendicular to y = -5x + 2.
A) k = -5
B) k = 14
C) k = 10
D) k = -10