Answer:
y = -1/2x
Explanation:
Currently, y = 2x - 5 is in slope-intercept form, whose general equation is y = mx + b, where
- (x , y) is any point on the line,
- m is the slope,
- and b is the y-intercept.
The slopes of perpendicular lines are negative reciprocals of each other. We can show this with the following 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.
Finding the slope of the other line:
Since 2 is the slope of y = 2x - 5, we can plug in 2 for m1 in perpendicular slope formula to find m2, the slope of the other line:
m2 = -1 / 2
m2 = -1/2
Thus, the slope of the other line is m = -1/2.
Finding the y-intercept of the other line:
We can find the y-intercept of the other line (i.e., b in the slope-intercept equation) by plugging in (-2, 1) for x and y and -1/2 for m in the slope-intercept form:
1 = -1/2(-2) + b
1 = 1 + b
0 = b
Thus, y = -1/2x is the line that passes through (-2, 1) and is perpendicular to y = 2x - 5.