Question

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

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

$m\times n=-1\\\\\Rightarrow -1\times n=-1\\\\\Rightarrow n=1.$

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.