Question

slopes of parallel/perpendicular lines
score: 2/5 penalty: 1 off
question
find the slope of a line perpendicular to the line whose equation is 6x + 15y = 225. fully simplify your answer.
answer attempt 1 out of 2
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Explanation:

Step1: Rewrite the given equation in slope - intercept form ($y = mx + b$, where $m$ is the slope)

We start with the equation $6x + 15y=225$.
Subtract $6x$ from both sides: $15y=-6x + 225$.
Divide each term by $15$: $y=\frac{-6}{15}x+\frac{225}{15}$.
Simplify the fractions: $y =-\frac{2}{5}x + 15$. So the slope of the given line ($m_1$) is $-\frac{2}{5}$.

Step2: Find the slope of the perpendicular line

The slope of a line perpendicular to a line with slope $m_1$ is the negative reciprocal of $m_1$. That is, if the slope of the given line is $m_1$, the slope of the perpendicular line ($m_2$) is $m_2=-\frac{1}{m_1}$.
Since $m_1 =-\frac{2}{5}$, then $m_2=-\frac{1}{-\frac{2}{5}}=\frac{5}{2}$.

Answer:

$\frac{5}{2}$