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)?

Answer 1

That line is in point-slope form:

$\sf y-y_1=m(x-x_1)$

Where 'm' is the slope and (x1, y1) is a point on the line.

Perpendicular lines have opposite slopes. To get the opposite, we take the reciprocal and multiply it by -1.

$\sf -1$

Reciprocal:

$\sf -\dfrac{1}{1}\rightarrow -\dfrac{1}{1}\rightarrow -1$

Multiply by -1:

$\sf 1$

We can plug this slope and the point into point-slope form, and then convert it to slope-intercept form.

$\sf y-y_1=m(x-x_1)$

$\sf y-(-2)=1(x-(-2))$

Negatives cancel out:

$\sf y+2=1(x+2)$

Distribute 1 into the parenthesis:

$\sf y+2=x+2$

Subtract 2 to both sides:

$\boxed{\sf y=x}$