Question

What is the equation, in slope-intercept form, of the line that is perpendicular to the line

y - 4 =--(x − 6) and passes through the point (-2, -2)?
-
0y=-²/3-x-100
O y=-2/x + 100
3
○ y = 2/x-1
O
Oy = ²2/x + 1
A

Answer 1

The equation, in slope-intercept form, of the line that is perpendicular to y - 4 = -(x - 6) and passes through the point (-2, -2) is y = x

Explanation:

To find the equation of the line that is perpendicular to the line y - 4 = -(x - 6) and passes through the point (-2, -2), we need to determine the slope of the given line and then find the negative reciprocal of that slope.

The given line is in the form y - 4 = -(x - 6). By rearranging the equation, we can identify the slope of the line.

y - 4 = -(x - 6)

y - 4 = -x + 6

y = -x + 10

The slope of the given line is -1.

Since the line we want to find is perpendicular to the given line, its slope will be the negative reciprocal of -1. The negative reciprocal of -1 is 1.

Now that we have the slope of the perpendicular line, we can use the point-slope form of a linear equation to find the equation of the line.

y - y1 = m(x - x1)

Using the point (-2, -2) and the slope of 1, we substitute the values into the point-slope form:

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

y + 2 = x + 2

Simplifying the equation, we have:

y = x