Find the slope of a line perpendicular to the line whose equation is 15, x, minus, 12, y, equals, 21615x−12y=216. Fully simplify your answer.
To find the slope of the line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.
The given line is in the form Ax + By = C, where A = 15, B = -12, and C = 216.
To find the slope of this line, we can rearrange the equation to solve for y:
15x - 12y = 216
-12y = -15x + 216
y = (15/12)x - 216/12
y = (5/4)x - 18
We can see that the coefficient of x is (5/4), so the slope of the given line is (5/4).
To find the slope of the line perpendicular to the given line, we take the negative reciprocal of (5/4):
negative reciprocal of (5/4) = -4/5
Therefore, the slope of the line perpendicular to the given line is -4/5.