Chapter 8, Problem 12CCSR

To determine

To calculate: the $\text{x}$ -intercept of the lines that passes through the points (0,-4) and (1, 4).

Answer to Problem 12CCSR

The option $\text{H}$ is correct $=\frac{1}{2}$ .

Explanation of Solution

Given information:

The $\text{x}$ -intercept of the lines that passes through the points (0,-4) and (1, 4).

Calculation:

Consider the points are (0,-4) and (1, 4)

According to line formula we find the $\text{x}$ -intercept that is

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

Here

  $\begin{array}{l}{x}_1=0\\ x_2=1\\ y_1=-4\\ y_2=4\end{array}$

Now put the points in given formula

  $\begin{array}{c}\left(y-y_1\right)=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\\ (y-(-4))=\frac{4-(-4)}{1-0}(x-0)\\ (y+4)=\frac{4+4}{1}(x)\\ y+4=8x\\ \frac{8}{8}x=\frac{y+4}{8}\\ x=\frac{1}{8}y+\frac{1}{2}\end{array}$

Then put the value $y=0$ for find the $x$ -intercept

  $\begin{array}{l}x=\frac{1}{8}y+\frac{1}{2}\\ =\frac{1}{8}(0)+\frac{1}{2}\\ =\frac{1}{2}\end{array}$

Therefore, the option $\text{H}$ is correct $=\frac{1}{2}$ .