Question

The table shows the cost to purchase school-spirit posters. Determine which kind of model best describes the data. Then write the equation.

No. of posters	2	4	6	8
Cost	4	7	10	13

Short answer

The equation of the function that models best the given data is $\mathit{y}\mathbf{=}\frac{\mathbf{3}}{\mathbf{2}}\mathit{x}\mathbf{+}\mathbf{1}$.

Step-by-step solution

Step 1. Determine the rate.

From the table it can be observed that as x increases by 2, the $y$increases by 3.

Therefore,

role="math" localid="1647851209614" $\begin{array}{l}\text{Rate}=\text{slope}\\ =\frac{\text{change\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{y}}{\text{change\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{x}}\\ =\frac{3}{2}\end{array}$

Step 2. Write an equation for the functions that models the data.

Since the rate is constant; the table of values represents a linear function of the form$y=ax+b$ . Since the rate is $\frac{3}{2}$, so $a=\frac{3}{2}$.

Step 3. Simplify the equation for the function.

To find $b$, use an ordered pair from the table, such as $(2,4)$.

role="math" localid="1647851305451" $\begin{array}{l}y=ax+b\\ 4=\frac{3}{2}\left(2\right)+b[x=2,y=4]\\ 4=3+b\\ b=1\\ y=\frac{3}{2}x+1\end{array}$

Therefore, the equation that models the data is $y=\frac{3}{2}x+1$.