Question

Find the rate of change of the linear function shown in the graph. Then find the initial value.

Answer 1

.................................

Answer 2

The rate of change is
`\( (3)/(5) \)` and the initial value is 0.

To find the rate of change (slope) of the linear function from the graph, you can use the formula:

`\[ \text{Slope (m)} = \frac{\text{Change in y}}{\text{Change in x}} = (y_2 - y_1)/(x_2 - x_1) \]`

From the graph, you need to select two points that the line passes through. Let's say we select the points (2, 1) and (7, 4).

Using these two points:

`\[ m = (4 - 1)/(7 - 2) = (3)/(5) \]`

So, the rate of change (slope) is
`\( (3)/(5) \).`

The initial value (y-intercept) is the value of y when x=0. Looking at the graph, the y-intercept appears to be at (0, 0).