Chapter 12, Problem 8CCSR

To determine

To find: the correct statement from the options which is the correct conclusion about the coordinates of the points on the graph.

Answer to Problem 8CCSR

The Option H statement is correct.

Explanation of Solution

Given:

  

Concept used:

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

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ .

Where, $\text{slope=m}=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

From the graph equation can be written as:

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ .

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

  $\begin{array}{l}\left(0,-2\right)\text{ and }\left(4,0\right).\\ \left(x_1,y_1\right)=\left(0,-2\right)\text{ and }\left(x_2,y_2\right)=\left(4,0\right).\\ y-\left(-2\right)=\frac{0-\left(-2\right)}{4-0}\left(x-0\right).\\ \Rightarrow y=\frac{x}{2}-2.\\ \Rightarrow 2y+4=x.\end{array}$

The equation of the graph is $2y+4=x.$

Option F is wrong since, $x$ value are $\text{4}$ digit greater than $y$ for all positive value of $y$ .

Option G is also wrong $y$ value is less than $x$ so, value of $\text{y}$ cannot be greater than $x$ .

Option H is true since, value $x$ is $\text{4}$ digit greater than $y$ for all positive value of $y$ .

Option I is false since, value of $y$ is less than $x$ so, value of $y$ cannot be greater than $x$ .

Hence, Option H statement is correct.