The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
From the information given,
The equation of the line to be determined is perpencicular to the line
y = -4x + 2
By comparing this equation with the slope intercept equation,
slope = - 4
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. The negative reciprocal of - 4 is 1/4. Thus, the slope of the line passing through (5, - 15/4) is 1/4. We would find the y intercept, c of this line by substituting m = 1/4, x = 5 and y = - 15/4 into the slope intercept equation. We have
- 15/4 = 1/4 * 5 + c
- 15/4 = 5/4 + c
c = - 15/4 - 5/4 = (- 15 - 5)/4 = - 20/4
c = - 5
By substituting m = 1/4 and c = - 5 into the slope intercept equation, the equation of the line that passes through (5, - 15/4) and is perpendicular to the line, y = - 4x + 2 is
y = x/4 - 5