Question

find the slope of a line perpendicular to the line whose equation is 6x + 15y = 225. fully simplify your answer.

Explanation:

Step1: Rewrite the given line in slope - intercept form

First, rewrite $6x + 15y=225$ as $y=mx + b$ form.
$15y=-6x + 225$, then $y=-\frac{6}{15}x+\frac{225}{15}$, so $y =-\frac{2}{5}x + 15$. The slope of this line $m_1=-\frac{2}{5}$.

Step2: Use the perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is $- 1$, i.e., $m_1\times m_2=-1$. Let the slope of the perpendicular line be $m_2$.
We have $-\frac{2}{5}\times m_2=-1$. Solving for $m_2$, we get $m_2=\frac{5}{2}$.

Answer:

$\frac{5}{2}$