Answer:
B: y = -(1/2)x + 4
Explanation:
I'll assume the x term is missing from options A and B:
IThey should read:
A. Y= - (1/2)x+ 8
B. Y= - (1/2)x+4
Use the two given points to calculate the slope of the line of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).
(0,4) and (8,0)
Rise = (0 - 4) = -4
Run = (8 - 0) = 8
Slope, m, = -4/8 or -(1/2)
The perpendicular line has the form y = -(1/2)x + b. There are options that have a -(1/2) slope: A and B.
To narrow it down, we need to calculate a value of b.
Use y = -(1/2)x + b and solve for b using either of the two given points [(0,4) or (8,0)]. I'll use (0,4).
y = -(1/2)x + b
4 = -(1/2)(0) + b
b = 4
The equation is thus y = -(1/2)x + 4, option B