Question

1. (l112) find the slope (rate of change) of line m, using the graph below.

a) -\frac{1}{5}
b) -\frac{1}{6}
c) -\frac{1}{7}
d) -\frac{1}{9}
e) none of the above

1. (l112) find slope (rate of change) of line n, using the graph above.

a) 1
b) 13
c) 4
d) 3
e) none of the above

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: Find slope of line M

For line M, we can use the points $(-3,2)$ and $(3,1)$. Then $x_1=-3,y_1 = 2,x_2=3,y_2 = 1$. Substitute into the slope formula: $m_M=\frac{1 - 2}{3-(-3)}=\frac{-1}{6}=-\frac{1}{6}$.

Step3: Find slope of line N

For line N, we can use the points $(0,-4)$ and $(1, - 1)$. Then $x_1 = 0,y_1=-4,x_2 = 1,y_2=-1$. Substitute into the slope formula: $m_N=\frac{-1-(-4)}{1 - 0}=\frac{-1 + 4}{1}=3$.

Answer:

1. b) $-\frac{1}{6}$
2. d) 3