91Ó°ÊÓ

The given table is:

Calculate the difference between $x$and $y$.

From the above table it can be noticed that the difference between $x$is 1 and the difference between $y$is $3.5$.

It can be noticed that the difference in values of$y$is constant. Therefore, the equation that represents the given data is the equation of the line.

The slope (m) of the line is given by:

$slope=\frac{16-12.5}{4-3}=3.5$

The equation of the line in slope-intercept is given by $y=mx+c$, where $m$is the slope of the line and $c$is the $y$-intercept.

The slope is $3.5$.

Therefore, the equation that represents the data in the table is given by $y=3.5x+c$

When $x=3,y=12.5$

$\begin{array}{c}y=3.5x+c\\ 12.5=3.5\left(3\right)+c\\ 12.5=10.5+c\\ 12.5−10.5=c\\ 2=c\end{array}$

Substitute the value $c$of in $y=3.5x+c$.

Therefore,$y=3.5x+2$

Therefore, the equation that represents the data in the table is $y=3.5x+2$.