Answer:
y = (1/4)x + 5
Explanation:
Lets rearrange the given equation into slope - intercept format of y = mx + b, where m is the slope and b is the y-intercept (the value of y when x is zero).
Line L: 4x + y = 7
y = -4x + 7
We find that the slope of line L, m, is -4.
A line perpendicular to L with have a slope that is the negative inverse of the slope of L. The negative inverse of -4 would be (1/4).
The new line, which we'll call P, will have the form of:
y = (1/4)x + b
Any line with a slope of (1/4) will be perpendicular to L.
But we want a line that also goes through point (-8,3). To make that happen, a value of b must be chosen to shift the line to (-8,3). The value of b that will do that can be calculated by entering that point in the equation y = (1/4)x + b:
y = (1/4)x + b
3 = (1/4)(-8) + b for (-8,3)
3 = -2 + b
b = 5
The line perpendicular to L and goes through (-8,3) is:
y = (1/4)x + 5
See the attached graph.