Chapter 4.2, Problem 16E

To determine

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

Answer to Problem 16E

Equation of line in slope intercept form is $y=\frac{1}{2}x-5$

Explanation of Solution

Given: Two points $\left(6,-2\right),\left(12,1\right)$

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 $\left(6,-2\right),\left(12,1\right)$

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:

  $\begin{array}{l}y-1=\frac{-2-1}{6-12}\left(x-12\right)\\ y-1=\frac{-3}{-6}\left(x-12\right)\\ y-1=\frac{1}{2}\left(x-12\right)\\ 2y-2=x-12\\ 2y=x-10\\ y=\frac{1}{2}x-5\end{array}$

Conclusion:

Hence, equation of line in slope intercept form is $y=\frac{1}{2}x-5$