Chapter 4, Problem 4CT

To determine

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

Answer to Problem 4CT

Equation of line in slope intercept formis $y=12$

Explanation of Solution

Given: line is parallel to line $y=\frac{2}{3}$ and passes through

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 a point and given slope is

  $y-y_1=m\left(x-x_1\right)$

Calculation:

Given that the line is parallel to line $y=\frac{2}{3}$

Since the line is parallel, thus slope of both lines must be equal

Thus, slope of line is given as

  $m=0$

Now, equation of line passing through a point and given slope is calculated as follows:

  $y-y_1=m\left(x-x_1\right)$

Substituting the values:

  $\begin{array}{l}y-12=0\left(x-\left(-4\right)\right)\\ y-12=0\left(x+4\right)\\ y-12=0\\ y=12\end{array}$

Conclusion:

Hence, equation of line is $y=12$