Question

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

A. y + 2 = -4(X+6)
B. V + 6 = -4(X+2) V
C. y +6 . ==1+2
D. 4-6-76-2​

Answer 1

The correct point-slope form for the line perpendicular to y = x-7 that passes through (-2, -6) is y + 6 = -1(x + 2), which, after correcting a typo, corresponds to Option B.

Step-by-step explanation:

To identify an equation in point-slope form for the line perpendicular to y = x - 7 that passes through (-2, -6), we first need to determine the slope of the given line. The slope of the line y = x - 7 is 1 since it is in the form y = mx + b where m is the slope. A line perpendicular to it would have a slope that is the negative reciprocal. Therefore, the slope of the perpendicular line is -1.

Using point-slope form, which is y - y1 = m(x - x1) where (x1, y1) is a point on the line and m is the slope, we can substitute the slope and the point (-2, -6) into the formula:

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

This equation can also be slightly rearranged to fit the given options:

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

Option B most closely approximates the correctly derived equation if we correct the typo 'V' to 'y' and the slope from -4 to -1.