Chapter 1.7, Problem 18HP

To determine

The equation which is the best

Answer to Problem 18HP

Option J is correct

Explanation of Solution

Given information:

  

The pair of points, $\left(3,7\right),\left(5,15\right)\text{,}\left(8,27\right)\text{and }\left(9,31\right)$

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 $\left(3,7\right),\text{ and }\left(5,15\right)$ , use the slope formula and substitute the values $\left(x_1,y_1\right)=\left(3,7\right),\text{ and }\left(x_2,y_2\right)=\left(5,15\right)$ and simplify further as shown below,

  $\begin{array}{c}\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{15-7}{5-3}\\ =\frac{8}{2}\\ =4\end{array}$

Thus, the slope of the line passing through the given points is $\text{4}$ .

So the equation for the graph is $y=4x-5$

Option J is correct