Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

Question

Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

Answer 1

The slope of the line given looks like 3 (3 up for every one across}

Parts a and b involve the same calculation, just in (a) the slope is 3 and in (b) it is -1/3

Here are 2 ways to do this: Equation of line through point in the form y = 3x + b (insert point and solve for b)

-2 = 3(3) +b b = -11 equation is y = 3x - 11

or you can use the a general definition of slope: 3 = (y+2)/(x-3) or point-slope y+2 = 3(x-3)

These all lead to same equation. I'll leave (b) to you.

Answer 2

I'll do b.

y = (-1/3)x + b

Plug in (3, -2)

-2 = -1/3 * 3 + b = -1 + b

-1 = b

The equation of the perpendicular line is y = (-1/3)x - 1