Q62. - Algebra 1

Question

Look for a pattern in each table of values to determine which kind of model best describes the data. Then write an equation for the function that models the data. 

 

$\mathit{x}$	0	1	2	3	4
$\mathit{y}$	3	6	9	12	15

Step-by-Step Solution

Answer

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

Step 1. Determine the rate.

For $x=0$ and $y=3$, this means $y$–intercept is 3. Note that as $x$ increases by 1, the $y$ increases by 3. Therefore,

 $\begin{array}{c}\text{Rate}=\text{slope}\\ =\frac{\text{change\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}y}{\text{change\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}x}\\ =\frac{3}{1}\\ =3\end{array}$

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 3, so $b=3$.

Step 3. Simplify the equation for the function.

To find $a$, use an ordered pair from the table, such as $(1, 6)$.

  $\begin{array}{l}y=ax+b\\ 6=a\left(1\right)+3 [x=1,y=6]\\ 6-3=a\\ a=3\\ y=3x+3\end{array}$ 

Therefore, the equation that models the data is $y=3x+3$.