Question

current learning objective: writing the equations of lines parallel or perpendicular to a given line
question 12
score: 0 of 1 point
what is the slope of the line perpendicular to the line that passes through the points (4,6) and (-1,1)?
slope: enter your answer
enter answer as integer or reduced fraction. do not use decimals.
submit answer attempts: 0/1
need help?
mathgpt isnt available for this question, but you can still master it! if your instructor enabled practice similar questions, youll get unlimited practice opportunities, plus ai tutoring if also enabled.
*ai ask mathgpt
ai tutoring is no longer available for this assignment.

Explanation:

Step1: Calculate slope of given line

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 4,y_1=6,x_2=-1,y_2 = 1$. So $m_1=\frac{1 - 6}{-1 - 4}=\frac{-5}{-5}=1$.

Step2: Find slope of perpendicular line

If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=-1$. Since $m_1 = 1$, we have $1\times m_2=-1$, so $m_2=-1$.

Answer:

$-1$