Question

Identify an equation in point-slope form for the line perpendicular to

y = x-7 that passes through (-2,-6).
A. y+6 = -1 (x + 2)
B. y-5-(-2)
C. y +6 = -4(x+2)
D. y +2 = -4(x+6)

Answer 1

The equation in point-slope form for the line perpendicular to y = x-7 that passes through (-2,-6) is y + 6 = -1(x + 2).

Step-by-step explanation:

To find the equation of a line perpendicular to y = x - 7 that passes through the point (-2, -6), we need to determine the slope of the original line and then find the negative reciprocal of that slope.

The slope of y = x - 7 is 1, so the slope of the perpendicular line is -1.

Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values x1 = -2, y1 = -6, and m = -1 into the equation and simplify to find the equation of the perpendicular line:

y - (-6) = -1(x - (-2))

y + 6 = -1(x + 2)

Therefore, the equation in point-slope form for the line perpendicular to y = x - 7 that passes through (-2,-6) is y + 6 = -1(x + 2) (option C).