Question

in 2 - 3, each table represents a linear relationship. choose two ordered pairs from the table and use the slope formula to find the rate of change. 2. x: 0, 1, 2, 3; y: 5, 5.5, 6, 6.5. 3. x: 3, 8, 11, 14; y: 15, 15, 15, 15. formula: (\frac{y_2 - y_1}{x_2 - x_1}) slope: __ formula: slope: __

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 ordered - pairs.

Step2: For table 2

Let $(x_1,y_1)=(0,5)$ and $(x_2,y_2)=(1,5.5)$. Then $m=\frac{5.5 - 5}{1 - 0}=\frac{0.5}{1}=0.5$.

Step3: For table 3

Let $(x_1,y_1)=(3,15)$ and $(x_2,y_2)=(8,15)$. Then $m=\frac{15 - 15}{8 - 3}=\frac{0}{5}=0$.

Answer:

For table 2: Formula: $m=\frac{y_2 - y_1}{x_2 - x_1}$, Slope: $0.5$
For table 3: Formula: $m=\frac{y_2 - y_1}{x_2 - x_1}$, Slope: $0$