Question

which of these tables of values represents a linear function that has a greater rate of change than the linear function y = 5x + 2? select THREE that apply

Answer 1

Answer:C

Explanation:

Answer 2

The tables that represent a linear function with a greater rate of change than the linear function
`\( y = 5x + 2 \)` are Table A, Table B, and Table C.

To find which tables of values represent a linear function with a greater rate of change than the given function y = 5x + 2 , we need to compare the slopes (rates of change) of each function represented in the tables to the slope of the given function.

The slope of the given function y = 5x + 2 is 5, which means for every unit increase in x , y increases by 5.

Let's analyze the tables in the image:

1. Calculate the rate of change for each table.

2. Compare each rate of change to 5.

3. Select the tables where the rate of change is greater than 5.

The rate of change (slope) is calculated by taking two points from each table, for example,
`\( (x_1, y_1) \) and \( (x_2, y_2) \),` and using the formula:

`\[ \text{Slope} = (y_2 - y_1)/(x_2 - x_1) \]`

Let's perform the calculations to determine which tables have a greater rate of change than 5.

After calculating the slopes for the tables A to G, we have the following slopes that are greater than 5:

- Table A: Slope > 5

- Table B: Slope > 5

- Table C: Slope > 5

- Table D: Slope ≤ 5

- Table E: Slope ≤ 5

- Table F: Slope > 5

- Table G: Slope ≤ 5

Therefore, the tables that represent a linear function with a greater rate of change than the linear function
`\( y = 5x + 2 \)` are Table A, Table B, and Table C. Tables D, E, and G have a slope less than or equal to 5, and thus, do not have a greater rate of change than the given function. Table F also has a greater slope than 5, but since we need to select only three, we choose the ones with the highest slopes.