Question

The following table shows the cost for a person to go to the 4 - H Fair to go on a certain number of rides: Develop an equation to represent the scenario. A. y = 2x + 5B. y = 6x C. y = -2.5xD. y = 8x + 26E. None of the above

Answer 1

In order to develop an equation, let's use the slope-intercept form of the linear equation:

$y=mx+b_{}$

Using the points (3, 13.5) and (5, 18.5) from the table, we have:

$\begin{gathered} (3,13.5)\colon \\ 13.5=3m+b \\ (5,18.5)\colon \\ 18.5=5m+b \end{gathered}$

Subtracting the second and the first equation:

$\begin{gathered} 5m+b-(3m+b)=18.5-13.5 \\ 2m=5 \\ m=2.5 \end{gathered}$

Now, finding the value of b:

$\begin{gathered} 13.5=3m+b \\ 13.5=7.5+b \\ b=13.5-7.5 \\ b=6 \end{gathered}$

So the equation that represents this table is y = 2.5x + 6

Looking at the options, the correct one is E (none of the above).