Q28. - 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. 

x	0	1	2	3	4
y	1	3	5	7	9

Step-by-Step Solution

Answer

The equation of the function that models best the given data is $y=2x+1$.

Step 1. Determine the rate .

For $x=0$ and $y=1$, this means y-intercept is 1. Note that as x increases by 1, the y increases by 2. Therefore, 

$$\begin{gathered} \text{Rate}=\text{slope} \\ =\frac{\text{change\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}y}{\text{change\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}x} \\ =\frac{2}{1} \\ =2 \end{gathered}$$

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 2, so $a=2$.

Step 3. Simplify the equation for the function.

To find b, use an ordered pair from the table, such as (1, 3).

 

$$\begin{gathered} y=ax+b \\ 3=2\left(1\right)+b[x=1,y=3] \\ 3-2=b \\ b=1 \\ y=2x+1 \end{gathered}$$

 

Therefore, the equation that models the data is $y=2x+1$.