Question

Y= - 4/3 x - 2
Find the equation of the line that is parallel and perpendicular to this line and that passes through the point (4,-3)
Y=?
Y=?

Answer 1

Well, first thing to do is to identify the slope of the given line. Use the fact that the line is in the slope-intercept form: \(y = mx+b\) where \(m\) is slope. From that, you find the slopes of the new lines. The parallel line will have identical slope. The perpendicular line will have slope -1/m because the product of the slopes of two perpendicular lines is -1.
Finally, use the equation for the line with slope \(m\) passing through point \((x_0,y_0)\) to write your new line equations:
\[y-y_0 = m(x-x_0)\]