Question

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 is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: Calculate 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 statement A is true.

Step3: Calculate slope of line $q$

For line $q$ with points $(6,15)$ and $(10,5)$, $m_q=\frac{5 - 15}{10 - 6}=\frac{-10}{4}=-\frac{5}{2}$. So statement B is true.

Step4: Calculate 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 statement C is false.

Step5: Calculate slope of line $p$

For line $p$ with points $(0,-2)$ and $(3,5)$, $m_p=\frac{5-(-2)}{3 - 0}=\frac{7}{3}$. So statement D is false.

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

$m_p\times m_q=\frac{7}{3}\times(-\frac{5}{2})=-\frac{35}{6}
eq - 1$. So statement E is false.

Answer:

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