Question

4.Which of these functions has the greatest rate of change?a. Y = 4x +17C. y = x + 7

Answer 1

Those equations are straight lines, in a line, the rate of change is represented by the slope. The slope intercept-form of a line is given by:

$\begin{gathered} y=mx+b \\ where \\ m=slope \\ b=y-intercept \end{gathered}$

So, for:

$\begin{gathered} y=4x+17 \\ m1=4 \end{gathered}$

for:

$\begin{gathered} y=x+7 \\ m2=1 \end{gathered}$

Since:

$\begin{gathered} m1>m2 \\ 4>1 \end{gathered}$

The function:

$y=4x+17$

has the greatest rate of change