Question

what is the rate of the change (m) for the table x. y-2. -3-1. 0 0. 31. 6

Answer 1

Step 1. To find the rate of change (or the slope) of the given table, we need to take two points (x,y) from the table.

We will take the first two points:

(-2,-3) and (-1,0)

Step 2. Label the points, for reference, as follows:

`\begin{gathered} x_1=-2_{}_{} \\ y_1=-3 \\ x_2=-1 \\ y_2=0 \end{gathered}`

Step 3. Use the rate of change formula:

`m=(y_2-y_1)/(x_2-x_1)`

Step 4. Substitute the values from step 2 into the formula from step 3:

`m=(0-(-3))/(-1-(-2))`

Step 5. Solve the operations:

We apply the law of signs: -(-)=+

`m=(0+3)/(-1+2)`

Then, solve the additions:

`m=(3)/(1)`

Finally, solve the division:

`m=3`

Answer:

The rate of change "m" is:

m=3