Answer:
So the equation of the line perpendicular to y=-x-7 and passing through (-2, -6) in point-slope form is y = x - 4.
Explanation:
To find the equation of a line perpendicular to y=-x-7, we need to find its slope first, which is the coefficient of x, which is -1 in this case. The slope of a line perpendicular to this line will be the negative reciprocal of this slope, so the slope of our line will be 1.
To find the equation of the line in point-slope form, we can use the formula:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line. We are given the point (-2, -6), so we can substitute these values into the formula and get:
y - (-6) = 1(x - (-2))
Simplifying this equation gives:
y + 6 = x + 2
Subtracting 6 from both sides gives:
y = x - 4
So the equation of the line perpendicular to y=-x-7 and passing through (-2, -6) in point-slope form is y = x - 4.