Question

1. which of the following represents the slope of the graph below?

a. -\frac{2}{3}
b. \frac{2}{3}
c. -\frac{3}{2}
d. - 10

1. find the slope, or rate of change, represented in the table below.

x	-1	0	1	2	3
y	-8	3	14	25	36

Explanation:

Step1: Recall slope formula

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

Step2: Solve for the slope of the graph

For the graph, let's take two points \((0, 10)\) and \((6, 4)\). Then \(m=\frac{4 - 10}{6-0}=\frac{-6}{6}=- 1\). But this is wrong. Let's take \((0,8)\) and \((6,4)\), then \(m=\frac{4 - 8}{6-0}=\frac{-4}{6}=-\frac{2}{3}\).

Step3: Solve for the slope of the table

Take two points from the table, say \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(1,14)\). Then \(m=\frac{14 - 3}{1-0}=\frac{11}{1}=11\). Let's use another pair, \((x_1,y_1)=(-1,-8)\) and \((x_2,y_2)=(0,3)\). Then \(m=\frac{3-(-8)}{0 - (-1)}=\frac{3 + 8}{1}=11\).

Answer:

1. A. \(-\frac{2}{3}\)
2. \(11\)