Chapter 4.2, Problem 20E

To determine

To calculate: To write the equation of line in slope intercept form that passes through the given points

Answer to Problem 20E

Equation of line in slope intercept form is $5y=-3x+80$

Explanation of Solution

Given: Two points $\left(-5,19\right),\left(5,13\right)$

Formula Used:

Equation of line in slope intercept form is given as:

  $y=mx+c$ , where

  $\begin{array}{l}m=slope\\ c=y-intercept\end{array}$

Also, equation of line passing through two points is given as

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

Calculation:

Given that the line passes through the points $\left(-5,19\right),\left(5,13\right)$

Thus, equation of line is calculated as follows:

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

Substituting the values:

  $\begin{array}{l}y-13=\frac{19-13}{-5-5}\left(x-5\right)\\ y-13=\frac{6}{-10}\left(x-5\right)\\ y-13=-\frac{3}{5}\left(x-5\right)\\ 5\left(y-13\right)=-3\left(x-5\right)\\ 5y-65=-3x+15\\ 5y=-3x+80\end{array}$

Conclusion:

Hence, equation of line in slope intercept form is $5y=-3x+80$