How do you find the slope of the line parallel to and perpendicular to y=3x-4?

Mar 1, 2017

Slope of line parallel is 3 while the slope of the perpendicular line is $- \frac{1}{3}$

Explanation:

The slope of any parallel is the slope of the original line.

For example: Given y = $\frac{2}{3} x$+5 the slope of a parallel line will be $\frac{2}{3}$ whereas the slope of a perpendicular line requires you to take the negative reciprocal of the slope.

Since the slope of this example is $\frac{2}{3}$ its negative reciprocal is $- \frac{3}{2}$ (You just flip the fraction and negate it)

Mar 1, 2017

$y$ has a slope of $3$

Explanation:

So any line with the same slope is parallel to $y$. They will be of the form $z = 3 x + b$, ($b$ being any number).

Perpendicular means that the product of the slopes must be $- 1$.

In this case the slope must be $- \frac{1}{3}$ because $- \frac{1}{3} \times 3 = - 1$

Any line of the form $p = - \frac{1}{3} x + b$ will do.