Chapter 4, Problem 2CT

To determine

To calculate: To write the equation of line in slope intercept form

Answer to Problem 2CT

Equation of line is $y=-3x+6$

Explanation of Solution

Given: Line passing through $\left(0,6\right)$ and $\left(3,-3\right)$

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 $\left(0,6\right)$ and $\left(3,-3\right)$

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:

  $\begin{array}{l}y-6=\frac{-3-6}{3-0}\left(x-0\right)\\ y-6=\frac{-9}{3}\left(x\right)\\ y-6=-3\left(x\right)\\ y-6=-3x\\ y=-3x+6\end{array}$

Conclusion:

Hence, equation of line is $y=-3x+6$