Question

Please help me figure this out.

Answer 1

The second choice and the fifth choice are correct.

Explanation:

y = x + 3 The rate of change for this equation is the number before the x. Since we do not see a number before the x, we assume that the number is 1, so the rate of change for this equation is 1.

Not the first choice:

To find the rate of change, you find the change in y over the change in x. You find the change by subtracting.

(-2,-7)(3,-2) The y values are -2 and-7. The x values are 3 and-2

`(-2-(-7))/(3 - (-2))` =
`(-2 + 7)/(3 + 2)` =
`(5)/(5)` = 1

This has the same rate of change as the equation (1)

The second choice is correct.

Select two points on the line. I have selected the points (0,1) and (1,3) To go from the first point to the second point, you need to go up 2 and left 1. This would be the rate of change of
`(2)/(1)` = 2. You will see people use the phrase rise over run. We rose 2 and we ran 1.

The rate of change is 2 which is greater than the rate of change in the equation of 1.

The Third choice in not correct.

The y is increasing by 1 and the x is increasing by 3. That gives a rate of change of
`(1)/(3)` which is less than 1.

The Fourth choice is not correct.

The rise is 1 and the run is 2. The rate of change is
`(1)/(2)` which is less than 1.

The Fifth choice is correct.

The y is changing by 9 and the x is changing by 6.
`(9)/(6)` is greater than 1.

Helping in the name of Jesus.