Chapter 1.4, Problem 8CFU

To determine

To find: line equation in slope-intercept form.

Answer to Problem 8CFU

  $y=\frac{7}{2}x-\frac{31}{2}$

Explanation of Solution

Given information:

The points on line are as follows:

  $\left(x_1,y_1\right)=\left(5,2\right)$

  $\left(x_2,y_2\right)=\left(7,9\right)$

Calculation

The point slope form is as follows:

  $y-y_1=m\left(x-x_1\right)$ … (1)

The equation slope is as follows:

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

Substitute the value of m in equation (1) to get,

  $y-y_1=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}\left(x-x_1\right)$ … (2)

Substitute the given points in equation (2) and simply it as follows:

  $\begin{array}{c}y-2=\frac{\left(9-2\right)}{\left(7-5\right)}\left(x-5\right)\\ y-2=\frac{7}{2}\left(x-5\right)\\ y-2=\frac{7}{2}x-\frac{35}{2}\\ y=\frac{7}{2}x-\frac{35}{2}-2\\ y=\frac{7}{2}x-\frac{35}{2}-2\left(\frac{2}{2}\right)\\ y=\frac{7}{2}x-\frac{35}{2}-\frac{4}{2}\\ y=\frac{7}{2}x-\frac{31}{2}\end{array}$

The slope intercept form is of the line is $y=\frac{7}{2}x-\frac{31}{2}$ .