What is the equation of a line that passes through the point (-7,2) and is perpendicular to the line whose equation is y = −2/5*x + 8?
The slope of our line y = x/4 + 5 is m = 1/4
Since we're coming up with the equation of a line that is perpendicular, the slope of our perpendicular line is the opposite reciprocal of 1/4, or m = - 4/1 or m = 4
Now, we need to find out the y-intercept of our perpendicular line. To do that we plug in (2, 7) into x and y as well as - 4 into m in the following equation:
y = mx + b
7 = (- 4)(2) + b
7 = - 8 + b
15 = b
Thus, with m = - 4 and b = 15, the equation of our perpendicular line is:
y = - 4x + 15
WARNING: Possibly wrong~ Hannah
Slope of given line is m = -2/5 perpindicular is - 1/m = 5/2
Point slope form of the new line through -7, 2 is y-2 = 5/2 ( x - -7)
y = 5/2 x + 35/2 +2
y = 5/2 x + 39/2
Here is a graph ( which I used as a check):
https://www.desmos.com/calculator/kvm5df9b2n