Chapter 1.7, Problem 14HP

To determine

The relation shown in the table.

Answer to Problem 14HP

The relation shown in the table is $\text{2}$

Explanation of Solution

Given information:

  

The pair of points, $\left(1,10\right),\text{ and }\left(2,12\right)$

Concept Used:

The slope of a line connecting the points $\left(x_1,y_1\right),\text{ and }\left(x_2,y_2\right)$ is given by the formula

  $\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

In order to find the slope of the line passing through the points $\left(1,10\right),\text{ and }\left(2,12\right)$ , use the slope formula and substitute the values $\left(x_1,y_1\right)=\left(1,10\right),\text{ and }\left(x_2,y_2\right)=\left(2,12\right)$ and simplify further as shown below,

  $\begin{array}{c}\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{12-10}{2-1}\\ =2\end{array}$

Thus, the relation shown in the table is $\text{2}$ .