how do I determine which equation represents a line that is perpendicular to line MN?
A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line falls through two closed points M (negative 7, 6), and N (5, 3).
A. y=-1/4x+9
B. y=1/4x+6
C. y=-4x-7
D. y=4x-6
To determine which equation represents a line that is perpendicular to line MN, we need to find the slope of line MN first.
The formula to find the slope between two points (x1, y1) and (x2, y2) is:
slope = (y2 - y1) / (x2 - x1)
Using the coordinates of M (x1 = -7, y1 = 6) and N (x2 = 5, y2 = 3):
slope = (3 - 6) / (5 - (-7))
slope = -3 / 12
slope = -1/4
Now, since the line we are looking for is perpendicular to line MN, the slope of the perpendicular line is the negative reciprocal of the slope of line MN.
The negative reciprocal of -1/4 is 4.
So, the equation representing a line perpendicular to line MN will have a slope of 4.
Comparing the given options:
A. y = -1/4x + 9 (slope = -1/4, not perpendicular)
B. y = 1/4x + 6 (slope = 1/4, not perpendicular)
C. y = -4x - 7 (slope = -4, not perpendicular)
D. y = 4x - 6 (slope = 4, perpendicular)
The equation that represents a line perpendicular to line MN is y = 4x - 6. Therefore, the correct answer is D.