Perpendicular equation

Question

Write an equation of the line that is perpendicular to 3x-4y=9 and contains (-4,-5)

Answer 1

Let's first find the slope of 3x - 4y = 9. Write this equation is terms of slope and intercept: y = mx + p

3x - 4y = 9 (add 4y to both sides)

3x = 4y + 9 (subtract 9 from both sides)

3x - 9 = 4y (divide both sides by 4)

y = (3/4)x - 9/4

So, slope is m=3/4. A perpendicular line's slope is -1/m. (Draw two perpendicular lines on a graph paper. Notice that, if one is increasing as x increases, the other decreases, which means it has negative slope. That is why we have the negative sign. Also, if one increase b units as x increases a units, the perpendicular line decreases a units as x increases b units, so if one has m = b/a the other has -a/b)

The perpendicular line is

y = (-4/3)x + p and needs to contain (-4,-5). Substitute x = -4 and y = -5 and solve for p:

-5 = (-4/3)*-4 + p

p = -5 - 16/3

p = -31/3

y = (-4/3)x = 31/3