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)?

A)y = –x –
B)y = –x +
C)y = x – 1
D)y = x + 1

Answer 1

y-4=-x + 6
y=-x+10
m=x
answer is D

Answer 2

Answer: The equation of the line in slope-intercept form is y = x.

Step-by-step explanation: We are given to find the equation in slope-intercept form of the line that is perpendicular to the line y - 4 = -(x - 6) and passes through the points (-2, -2).

PERPENDICULAR LINES: The product of the slopes of two perpendicular lines is -1.

The slope-intercept form of the given line is

`y-4=-(x-6)\\\\\Rightarrow y-4=-x+6\\\\\Rightarrow y=-x+6+4\\\\\Rightarrow y=-x+10.`

So, slope of the line, m = co-efficient of x = 1.

Let 'n' be the slope of the perpendicular line, so we have

`m* n=-1\\\\\Rightarrow -1* n=-1\\\\\Rightarrow n=1.`

Therefore, the slope-intercept form of the line with slope n = 1 and passing through the point (-2, -2) will be

`y-(-2)=n\{x-(-2)\}\\\\\Rightarrow y+2=x+2\\\\\Rightarrow y=x.`

Thus, the slope-intercept form of the line is y = x.