Question

Which lines are perpendicular to the line y - 1 = 1(x+2)? Check all that apply.

Answer 1

The general equation of the lines that are perpendicular is:

`y=-x+b`

b can by any number.

Explanation:

The equation of a line is given by:

`y=mx+a`

where m is the slope and b is the intercept

The equation of a perpendicular line to the previuos one is:

`y=- (1)/(m) x+b`

That means that the slope of a perpendicular line is inverse and sign opposite to the other line.

Hence, the equation given is:

`y - 1 = 1(x+2) \\ y=x+2+1 \\ y=x+3`

m would be:

m=1

So the perpendicular slope would be:

`- (1)/(m)=- (1)/(1) =-1`

The general equation of the lines that are perpendicular to y=x+3 is:

`y=-x+b`

b can be any number

In attached picture:

y=x+3 is the red line

y=-x+b is the blue line