Question

Given the graph of a line y=−x.

Answer 1

Answer: $y=x-6$

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

By definition, the slopes of perpendicular lines are negative reciprocals.

Given the line:

$y=-x$

We know that a line perpendicular to this line must have this slope:

$m=\frac{1}{1}=1$

Since that line goes through the point (8,2), we can substitute the slope 1 and these coordinates into $y=mx+b$ and solve for "b":

$2=(1)(8)+b\\\\2-8=b\\\\b=-6$

Therefore, the equation of this line is:

$y=x-6$