Question

Give the slope of a line perpendicular to the given line. $$ y=-4 x+2 $$

Short answer

The slope of the line perpendicular to the given line is \(\frac{1}{4}\).

Step-by-step solution

Identify the slope of the given line

The equation of the given line is in the form \(y = mx + n\), where \(m\) is the slope. So, the slope \(m\) of the given line is -4.

Calculate the slope of the perpendicular line

The slope of the line perpendicular to the given line would be the negative reciprocal of the given line's slope. The negative reciprocal of -4 is calculated as follows: flip the fraction (4 becoming \(\frac{1}{4}\)) and change the sign (positive to negative or negative to positive, so -4 becomes \(\frac{1}{4}\)). Hence, the slope of the line perpendicular to the given line is \(\frac{1}{4}\).

Confirm the Result

To confirm, check if the product of the slope of the given line and the slope of the line perpendicular is -1. The product is (-4) * (\(\frac{1}{4}\)) = -1, so the result is correct.