Question

Given the equation of a line y = 5x -16, what is the slope of a line PERPENDICULAR to this line?​

Answer 1

Answer:

$-\frac{1}{5}$

Step-by-step explanation:

Notice that the equation y = 5x - 16 is in slope-intercept form, or $y = mx + b$ format. Whenever an equation is in slope-intercept form, the number in place of the $m$, or the coefficient of the x-term, represents the slope of that line. So, the slope of the given line is 5.

Slopes that are perpendicular to each other are opposite reciprocals. So, we need to find the opposite reciprocal of 5. To do that, write it as a fraction, making it $\frac{5}{1}$. Then, switch the sign and flip the numerator and denominator. This means that the opposite reciprocal of 5 is $-\frac{1}{5}$, so $-\frac{1}{5}$ is the perpendicular slope.