Chapter 8.3, Problem 39WE

To determine

To calculate: The slope of line through the points,

  $\left(4,6\right),\left(0,4\right),\left(8,y\right)$

Find the value of $y$ lies on this line.

Answer to Problem 39WE

The slope of the line is: $\frac{1}{2}$ .

The value of $y$ is: $8$ .

Explanation of Solution

Given information:

The points of the lines:

  $\left(4,6\right),\left(0,4\right),\left(8,y\right)$

Formula used:

For finding the slope of the line:

  $m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

Consider the points,

  $\left(4,6\right),\left(0,4\right),\left(8,y\right)$

For finding the slope of line,

Apply the formula to find the slope a line whose vertices are:

  $\left(4,6\right),\left(0,4\right)$

  $m=\frac{y_2-y_1}{x_2-x_1}$

Now finding the values of $x_1,x_2,y_1,y_2$ from the points $\left(4,6\right),\left(0,4\right)$ .

The values are:

  $\begin{array}{l}{x}_1=4,y_1=6\\ x_2=0,y_2=4\end{array}$

Apply the values in the formula now:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{4-6}{0-4}\\ m=\frac{-2}{-4}\\ m=\frac{1}{2}\end{array}$

Now find the slope between the points $\left(8,y\right),\left(4,6\right)$ and get it equal to the slope $\frac{1}{2}$ .

  $m=\frac{y_2-y_1}{x_2-x_1}$

Now finding the values of $x_1,x_2,y_1,y_2$ from the points $\left(8,y\right),\left(4,6\right)$ .

The values are:

  $\begin{array}{l}{x}_1=8,y_1=y\\ x_2=4,y_2=6\end{array}$

Apply the values in the formula now:

  $\begin{array}{c}\frac{y_2-y_1}{x_2-x_1}=m\\ \frac{y-6}{8-4}=\frac{1}{2}\\ \frac{y-6}{4}=\frac{1}{2}\end{array}$

Now by the cross multiplication:

  $\begin{array}{c}\frac{y-6}{4}=\frac{1}{2}\\ y-6=\frac{4}{2}\\ y-6=2\\ y=2+6\\ y=8\end{array}$

Thus,

The slope of the line is: $\frac{1}{2}$ .

The value of $y$ is: $8$ .