Question

what is the slope of a line perpendicular to the line graphed, written as a fraction? a line is graphed in the coordinate plane. enter the answer in the space provided. fractions should be entered in lowest terms using a forward slash (/) and converted to improper fractions when applicable. use only numbers, a negative sign (-), a decimal point (.), and/or a forward slash (/) to enter the answer.

Explanation:

Step1: Find the slope of the given line

Pick two points on the given line, say $(0, - 1)$ and $(4,0)$. Using the slope - formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we have $m_1=\frac{0-( - 1)}{4 - 0}=\frac{1}{4}$.

Step2: Use the perpendicular - slope relationship

If two lines are perpendicular, the product of their slopes is $-1$, i.e., $m_1\times m_2=-1$. Given $m_1 = \frac{1}{4}$, then $\frac{1}{4}\times m_2=-1$. Solving for $m_2$, we get $m_2=-4$.

Answer:

$-4$