Question

Given the graph of a line y=−x.

b
Write an equation of a line which is perpendicular and goes through the point (8,2).

Answer 1

Answer:
`y=x-6`

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=(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`