The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
By comapring the given equation,
slope, m = 1/2
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Thus,
slope of line passing through (8, - 7) = - 2/1 = - 2
We would find the y intercept of the line passing through (8, - 7) by substituting x = 8, y = - 7 and m = - 2 into the slope intercept equation. We have
- 7 = - 2 * 8 + c
- 7 = - 16 + c
c = - 7 + 16 = 9
The equation of the line is
y = - 2x + 9