Question

What is the equation of the line perpendicular to the line y = four over nine x – 2 that passes through the point (4,3)?

Answer 1

Let's take a look at the frist problem. 2 and 3 can be solved the same way.

First of all you have to rewrite your equation 3x + y = 5 (this is a standard form) in slope-intercept form by subtracting 3x from both sides of the equation. We have y = -3x +5. That means the sloppe of the line is

m=-3 (if we use y = mx+b form of the linear equation). The line which is perpendicular to that will have the slope equal to the reciprocal of (-3) taken with negative sign. Thus, the  new slope equals 1/3. Or your equation for the perpendicular line should be like

                                                           y = (1/3)x +b

In order to find "b" use the point given in the problem. If x =-9 y =3. Thus, we have

                                   3 = (1/3)(-9) +b = -3 +b        or b = 3+3 =6

The equation for  a perpendicular line becomes

                                            y = (1/3)x +6

Repeat the same steps for problems 2 and 3.