Questions: Tyler: Aubri: y = 3/2 x x (seconds) y (meters) 0 0 4 6 8 12 12 18 Who has the greater rate of change?

Transcript text: Tyler: Aubri: $y=\frac{3}{2} x$ \begin{tabular}{|c|c|} \hline$x$ (seconds) & $y$ (meters) \\ \hline 0 & 0 \\ \hline 4 & 6 \\ \hline 8 & 12 \\ \hline 12 & 18 \\ \hline \end{tabular} Who has the greater rate of change?

Solution

Solution Steps

To determine who has the greater rate of change, we need to compare the slopes of the lines representing Tyler's and Aubri's data. The slope of a line is the rate of change. For Aubri, the slope is given directly by the equation $ y = \frac{3}{2} x $. For Tyler, we can calculate the slope using the given data points.

Solution Approach

Calculate the slope for Tyler using the formula $ \text{slope} = \frac{\Delta y}{\Delta x} $ with the given data points.
Compare the slope of Tyler's line to the slope of Aubri's line.

Step 1: Calculate Tyler's Slope

Using the data points for Tyler, we calculate the slope $ m_T $ as follows: \[ m_T = \frac{y_2 - y_1}{x_2 - x_1} = \frac{18 - 0}{12 - 0} = \frac{18}{12} = 1.5 \]

Step 2: Identify Aubri's Slope

Aubri's slope $ m_A $ is given directly from the equation $ y = \frac{3}{2} x $: \[ m_A = \frac{3}{2} = 1.5 \]

Step 3: Compare the Slopes

Now we compare the slopes: \[ m_T = 1.5 \quad \text{and} \quad m_A = 1.5 \] Since $ m_T = m_A $, both Tyler and Aubri have the same rate of change.