Question

question what is the slope of the line that is perpendicular to the line shown on the graph? answer attempt 1 out of 2

Explanation:

Step1: Find slope of given line

Pick two points on the line, say $(- 8,0)$ and $(0,5)$. Use slope - formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m_1=\frac{5 - 0}{0-(-8)}=\frac{5}{8}$.

Step2: Use perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is $-1$, i.e., $m_1\times m_2=-1$. Given $m_1 = \frac{5}{8}$, then $\frac{5}{8}\times m_2=-1$. Solving for $m_2$, we get $m_2=-\frac{8}{5}$.

Answer:

$-\frac{8}{5}$