Question

for items 1-2, use the figure shown. select all the true statements. a. the slope of m is -\frac{2}{5}. b. the slope of q is -\frac{5}{2}. c. the slope of n is \frac{2}{5}. d. the slope of p is -\frac{5}{2}.

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 $(3,5)$, we have $x_1=-2,y_1 = 7,x_2=3,y_2 = 5$. Then $m_m=\frac{5 - 7}{3-(-2)}=\frac{-2}{5}=-\frac{2}{5}$, so statement A is true.

Step3: Calculate slope of line $q$

For line $q$ with points $(6,15)$ and $(10,5)$, we have $x_1 = 6,y_1=15,x_2 = 10,y_2=5$. Then $m_q=\frac{5 - 15}{10 - 6}=\frac{-10}{4}=-\frac{5}{2}$, so statement B is true.

Step4: Calculate slope of line $n$

For line $n$ with points $(-5,0)$ and $(0,-2)$, we have $x_1=-5,y_1 = 0,x_2=0,y_2=-2$. Then $m_n=\frac{-2-0}{0-(-5)}=-\frac{2}{5}
eq\frac{2}{5}$, so statement C is false.

Step5: Calculate slope of line $p$

For line $p$ with points $(3,5)$ and $(6,15)$, we have $x_1 = 3,y_1=5,x_2 = 6,y_2=15$. Then $m_p=\frac{15 - 5}{6 - 3}=\frac{10}{3}
eq-\frac{5}{2}$, so statement D is false.

Answer:

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