Question

This graph represents the linear relationship between the time in minutes and Olivia's elevation in meters. For each minute, her elevation increases at a constant rate. After 4 minutes, Olivia’s elevation is 140 meters. After 8 minutes, her elevation is 260 meters. Let’s write an equation to represent this line in the form y=mx+b. Start by finding m, or the slope. What is the slope of this line? In other words, what is Olivia’s change in elevation for each minute?

Answer 1

To find the slope \( m \) of the linear relationship between time in minutes and elevation in meters, we can use the formula for the slope:

\[
m = \frac{\Delta y}{\Delta x}
\]

where \( \Delta y \) is the change in elevation, and \( \Delta x \) is the change in time.

From the information provided:

- After 4 minutes, Olivia’s elevation is 140 meters.
- After 8 minutes, Olivia’s elevation is 260 meters.

Now we calculate the changes:

\[
\Delta y = 260 \text{ m} - 140 \text{ m} = 120 \text{ m}
\]
\[
\Delta x = 8 \text{ min} - 4 \text{ min} = 4 \text{ min}
\]

Now we can calculate the slope \( m \):

\[
m = \frac{120 \text{ m}}{4 \text{ min}} = 30 \text{ m/min}
\]

Therefore, the slope \( m \), which represents Olivia's change in elevation for each minute, is \( 30 \) meters per minute.