Q15. - Algebra 1

Question

Write an equation that represents the data in the table.

x	y
3	12.5
4	16
5	19.5
6	23
7	26.5

Step-by-Step Solution

Answer

The equation that represents the data in the table is $\mathit{y}\mathbf{=}\mathbf{3}\mathbf{.5}\mathit{x}\mathbf{+}\mathbf{2}$

Step 1. Observe the table.

The given table is:

x	y
3	12.5
4	16
5	19.5
6	23
7	26.5

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

x	y
3	12.5
4	16
5	19.5
6	23
7	26.5

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: 

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

Step 2. Write an equation that represents the data in the table.

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 $y=3.5x+2$.