Question

1. which of the following represents the slope of the graph below? a. -2/3 b. 2/3 c. -3/2 d. -10 2. 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 between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: For the graph in question 1

Let's take two points on the graph, say $(3,8)$ and $(9,4)$. Then $x_1 = 3,y_1=8,x_2 = 9,y_2 = 4$.
$m=\frac{4 - 8}{9 - 3}=\frac{-4}{6}=-\frac{2}{3}$.

Step3: For the table in question 2

Let's take two points from the table, say $(x_1=-1,y_1 = - 8)$ and $(x_2=0,y_2 = 3)$.
$m=\frac{3-(-8)}{0 - (-1)}=\frac{3 + 8}{1}=11$.

Answer:

1. a. $-\frac{2}{3}$
2. 11