Question

Which linear function has the greater rate of change, the one described by the equation y = 3x + 4 or the one described by the table? 1 WN X у 3 10 17 24 4 Choose the correct answer below. O A. The function for the table has the greater rate of change. OB. The function y = 3x + 4 has the greater rate of change.Table:x y1 32 103 174 24

Answer 1

The rate of change is equivalent to the slope in linear functions.

So, the bigger the slope, the greater the rate of change.

In the case of the linear function y=3x+4, the slope is m=3.

In the case of the table, we have to select two points in order to calculate the slope m.

We will pick the points (1,3) and (2,10).

Then, we can calculate the slope as:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{10-3}{2-1}=\frac{7}{1}=7$

As the slope of the function in the table is bigger than the slope of the function y=3x+4, the function from the table has a greater rate of change.

$\begin{gathered} m_t>m_f \\ 7>3 \end{gathered}$

Answer: Option A (The function for the table has the greater rate of change)