Question

find the slope between the two points. then identify the line that has perpendicular slope. (-2,3) (4,1) a. y=-1/3x+3 b. y=3x-2 c. y=-0.5x+3 d. y=-x+1/3

Explanation:

Step1: Recall slope - formula

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, $(x_1,y_1)=(-2,3)$ and $(x_2,y_2)=(4,1)$.

Step2: Calculate the slope

$m=\frac{1 - 3}{4-(-2)}=\frac{-2}{6}=-\frac{1}{3}$.

Step3: Recall perpendicular - slope relationship

If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=-1$. Let the slope of the given line be $m =-\frac{1}{3}$, and the slope of the perpendicular line be $m_p$. Then $-\frac{1}{3}\times m_p=-1$, so $m_p = 3$.

Step4: Identify the line with the perpendicular slope

The equation of a line is in the form $y = mx + b$, where $m$ is the slope. Among the options, the line $y = 3x-2$ has a slope of $3$.

Answer:

B. $y = 3x-2$