Chapter 12, Problem 6CCSR

To determine

To find: the table models from the option which can form the given graph and write the correct answer on the paper.

Answer to Problem 6CCSR

The option $\text{G}$ table holds the correct table for the graph.

Explanation of Solution

Given:

  

Concept used:

The equation can be find using two points formula from the straight line:

  ${\text{y-y}}_1\text{=}\frac{{\text{y}}_2{\text{-y}}_1}{{\text{x}}_2{\text{-x}}_1}\left({\text{x-x}}_1\right)$ .

Where, $\text{slope=m}=\frac{{\text{y}}_2{\text{-y}}_1}{{\text{x}}_2{\text{-x}}_1}$ .

The two point can be deduced from graph by taking the intersection of straight line with x-axis and y-axis respectively.

Calculation:

From the graph equation can be written as:

  ${\text{y-y}}_1\text{=}\frac{{\text{y}}_2{\text{-y}}_1}{{\text{x}}_2{\text{-x}}_1}\left({\text{x-x}}_1\right)$ .

The graph x-axis and y-axis intersect at two point which are:

  $\begin{array}{l}\left(-4,0\right)\text{ and }\left(0,2\right).\\ \left({\text{x}}_1{\text{,y}}_1\right)=\left(-4,0\right)\text{ and }\left({\text{x}}_2{\text{,y}}_2\right)=\left(0,2\right).\\ \text{y-}0\text{=}\frac{2-0}{0-\left(-4\right)}\left(\text{x-}\left(-4\right)\right).\\ \Rightarrow \text{y=}\frac{1}{2}\left(\text{x+}4\right).\end{array}$

The equation of the graph is $\text{y=}\frac{1}{2}\left(\text{x+}4\right)$ .

From option $\text{A}$ Point $\left(1,3\right)$ is not in the line since, it didn’t satisfy the equation.

From option $\text{C}$ point $\left(4,4\right)$ is only point which lies in line since, it’s satisfies the equation.

From option $\text{D}$ none of the points are on the line.

From option $\text{G}$ all point lie in the line.

Hence, option $\text{G}$ table holds the correct table for the graph.