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

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Answer 1 · 2016-11-07T17:11:57

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

Given: $5 x + 2 y = 8$ $5x + 2y = 8$

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

Subtract 5x from both sides:

$2 y = - 5 x + 8$ $2y = -5x + 8$

Divide both sides by 2:

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

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

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

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

$n = - \frac{1}{- \frac{5}{2}}$ $n = -1/(-5/2)$

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

How do you find the slope that is perpendicular to the line 5x+2y=85x+2y=8?