Question

What is the equation of a line that is perpendicular to -x+3y=9 and passes through point (-3,2)

Answer 1

Answer:

The perpendicular line would be y = -3x - 7

Step-by-step explanation:

To find the equation of the line, we first need to solve the original line for y.

-x + 3y = 9

3y = x + 9

y = 1/3x + 3

Now we know the slope of the original line to be 1/3. Since perpendicular lines have opposite and reciprocal slope, we know the new line to have a slope of -3. We can then use that along with the given point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 2 = -3(x + 3)

y - 2 = -3x - 9

y = -3x - 7