Question

Use the graph to identify the following.
The Graph shows a graph that gos from y :80 to 320, and x being 2 to 8

there is a dot at x 2 and y 80, x 4 and y 60, x 6 and y 240
Rate of Change
(2 points)

The slope of the function is m=

.

The equation can be written as y=

where x represents time in hours and y represents distance.

Answer 1

To find the rate of change (slope) and to write the equation of the line, we need to examine the points provided in the graph: (2, 80), (4, 60), and (6, 240).

### Step 1: Calculate the Slope (Rate of Change)

The slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

We can use the points (2, 80) and (6, 240) to calculate the slope.

Using point (2, 80) as \((x_1, y_1)\) and (6, 240) as \((x_2, y_2)\):

\[
m = \frac{240 - 80}{6 - 2} = \frac{160}{4} = 40
\]

### Step 2: Write the Equation of the Line

Using the slope-intercept form of the equation of a line, which is:

\[
y = mx + b
\]

We have \(m = 40\). We need to find \(b\), the y-intercept. We can use one of the points provided; let's use (2, 80):

\[
80 = 40(2) + b
\]

\[
80 = 80 + b
\]

\[
b = 80 - 80 = 0
\]

So, the y-intercept \(b = 0\).

Now we can write the equation:

\[
y = 40x
\]

### Summary

- The slope of the function is \(m = 40\).
- The equation can be written as \(y = 40x\), where \(x\) represents time in hours and \(y\) represents distance.