Answer:
-4/5
Explanation:
To find the slope of a line perpendicular to the line with the equation 15x - 12y = 216, we can follow these steps:
Step 1: Rewrite the given equation in slope-intercept form, y = mx + b, where m represents the slope of the line:
15x - 12y = 216
First, subtract 15x from both sides:
-12y = -15x + 216
Then, divide both sides by -12 to solve for y:
y = (15/12)x - 18
Simplifying further, we have:
y = (5/4)x - 18
Step 2: Identify the slope of the given line. In this case, the coefficient of x in the slope-intercept form is (5/4), which represents the slope.
Step 3: Determine the slope of a line perpendicular to the given line. The slopes of perpendicular lines are negative reciprocals of each other. To find the negative reciprocal of (5/4), we flip the fraction and change the sign:
Negative reciprocal of (5/4) = -4/5
Therefore, the slope of a line perpendicular to the line with the equation 15x - 12y = 216 is -4/5.