Chapter SH, Problem 8.8.9EP

To determine

To calculate: To write the equation in slope-intercept form for the line passing through the pair of points

Answer to Problem 8.8.9EP

Equation of line in slope-intercept form is $y=\frac{4}{5}x+\frac{33}{5}$

Explanation of Solution

Given information: Pair of points are $\left(-2,5\right)$ and $\left(3,9\right)$

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Slope of line using two points is given as

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

Calculation:

Given the pair of points are $\left(-2,5\right)$ and $\left(3,9\right)$

Using the two-point equation of line,

  $\begin{array}{l}y-9=\frac{5-9}{-2-3}\left(x-3\right)\\ y-9=\frac{-4}{-5}\left(x-3\right)\\ -5\left(y-9\right)=-4\left(x-3\right)\\ -5y+45=-4x+12\\ -5y=-4x+12-45\\ -5y=-4x-33\\ y=\frac{-4}{-5}x+\frac{-33}{-5}\\ y=\frac{4}{5}x+\frac{33}{5}\end{array}$

Conclusion:

Hence, equation of line in slope-intercept form is $y=\frac{4}{5}x+\frac{33}{5}$