The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The equation of the given line is
y = 4x - 7
Slope, m = 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. This means tha the slope of the line that crosses the point (-4,6) is - 1/4
To find the y intercept of the equation of this line, we would substitute m = 4, x = - 4 and y = 6 into the slope intercept equation. It becomes
6 = - 1/4 * - 4 + c
6 = 1 + c
c = 6 - 1 = 5
We would substitute m = - 1/4 and c = 5 into the slope intercept equation. The equation of the line would be
y = - x/4 + 5