Answer:
y = -2/9x - 7
Explanation:
The slopes of perpendicular lines are negative reciprocals of each other, as shown by the formula m2 = -1/m1, where
- m2 is the slope of the line we're trying to find,
- and m1 is the slope of the line we're given
The line y = 9/2x + 2 is in slope-intercept form (y = mx + b), where
- m is the slope,
- and b is the y-intercept
Step 1: Thus, our m1 value (the slope of the given line) is 9/2 and we can plug it into the perpendicular slope formula to find m1 (the slope of the line we're trying to find):
m2 = -1 / (9/2)
m2 = -1 * 2/9
m2 = -2/9
Thus, the slope of the second line is -2/9.
Step 2: We can find b, the y-intercept of the second line by using the slope-intercept form and plugging in (-9, -5) for x and y and -2/9 for m:
-5 =-2/9(-9) + b
-5 = 18/9 + b
-5 = 2 + b
-7 = b
Thus, the y-intercept of the second line is -7
Thus, the equation of the line that passes through (-9, -5) and is perpendicular to the line y = 9/2x + 2 is y = -2/9x - 7