Chapter 4.3, Problem 26MR

To determine

To check: Whether the provided relationship is a linear function or not. Also, show the relationship using the words, graphs and equation

Explanation of Solution

Given:

The table is:

x	y
0	3
1	5
2	7
3	9

Calculation:

Here, it could be seen that there is a change of 2 unit in the variable y. Thus, it could be said that the function is linear.

The equation of the line could be written as:

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ m\text{ is the slope}\end{array}$

Slope could be calculated as:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{5-3}{1-0}\\ =2\end{array}$

The equation of the line could be constructed as:

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-3=2\left(x-0\right)\\ y=2x+3\end{array}$

Graph:

The figure could be constructed as: