Question

for items 1 - 2, use the figure shown. select all the true statements. a the slope of m is - 2/5. b the slope of q is - 5/2. c the slope of n is 2/5. d the slope of p is - 5/2. e the product of the slopes of p and q is - 1.

Explanation:

Step1: Recall slope formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Find slope of line $m$

For line $m$ with points $(-2,7)$ and $(3,5)$, $m_m=\frac{5 - 7}{3-(-2)}=\frac{-2}{5}=-\frac{2}{5}$. So option A is true.

Step3: Find slope of line $q$

For line $q$ with points $(0, - 2)$ and $(10,5)$, $m_q=\frac{5-(-2)}{10 - 0}=\frac{7}{10}$. So option B is false.

Step4: Find slope of line $n$

For line $n$ with points $(-5,0)$ and $(0,-2)$, $m_n=\frac{-2 - 0}{0-(-5)}=-\frac{2}{5}$. So option C is false.

Step5: Find slope of line $p$

For line $p$ with points $(3,9)$ and $(6,15)$, $m_p=\frac{15 - 9}{6 - 3}=2$. So option D is false.

Step6: Check product of slopes of $p$ and $q$

$m_p\times m_q=2\times\frac{7}{10}=\frac{7}{5}
eq - 1$. So option E is false.

Answer:

A. The slope of $m$ is $-\frac{2}{5}$