Question

Use the graph to identify the following.

Rate of Change two points on the graph are 80,2 and 160,4

(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 slope (rate of change) between the two points \((80, 2)\) and \((160, 4)\), we can use the formula for slope:

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

Here, \((x_1, y_1) = (80, 2)\) and \((x_2, y_2) = (160, 4)\).

Substituting the values:

\[
m = \frac{4 - 2}{160 - 80} = \frac{2}{80} = \frac{1}{40}
\]

So, the slope of the function is \(m = \frac{1}{40}\).

Now, we can write a linear equation in the slope-intercept form \(y = mx + b\). We know the slope \(m\) and can use one of the points to solve for \(b\).

Using point \((80, 2)\):

\[
2 = \frac{1}{40}(80) + b
\]

Calculating:

\[
2 = 2 + b
\]
\[
b = 2 - 2 = 0
\]

Thus, the equation for the line is:

\[
y = \frac{1}{40}x + 0 \implies y = \frac{1}{40}x
\]

Putting everything together:

- The slope of the function is \(m = \frac{1}{40}\).
- The equation can be written as \(y = \frac{1}{40}x\), where \(x\) represents time in hours and \(y\) represents distance.