Find the slope of a line perpendicular to the line whose equation is 5, x, minus, 4, y, equals, minus, 245x−4y=−24. Fully simplify your answer.
To find the slope of the line given by the equation 5x - 4y = -24, we need to rewrite it in slope-intercept form, which is y = mx + b.
First, isolate y:
5x - 4y = -24
-4y = -5x - 24
y = (5/4)x + 6
The slope of the line is 5/4.
The slope of a line perpendicular to this line is the negative reciprocal of 5/4.
Reciprocal of 5/4 is 4/5
Negative reciprocal of 5/4 is -4/5.
Therefore, the slope of a line perpendicular to the line given by the equation 5x - 4y = -24 is -4/5.