How do you find the slope that is perpendicular to the line 5x+2y=8?

Nov 7, 2016

Please see the explanation for steps leading to the slope of any perpendicular line equal to $\frac{2}{5}$

Explanation:

Given: $5 x + 2 y = 8$

Rewrite the equation of the line in slope-intercept form, $y = m x + b$.

Subtract 5x from both sides:

$2 y = - 5 x + 8$

Divide both sides by 2:

$y = - \frac{5}{2} x + 4$

Please observe that the slope, $m = - \frac{5}{2}$.

The slope, n, of a perpendicular line will be:

$n = - \frac{1}{m}$

$n = - \frac{1}{- \frac{5}{2}}$

$n = \frac{2}{5}$