Chapter 4.3, Problem 12E

To determine

To calculate: To write the equation of line that passes through the given point and is parallel to the given line

Answer to Problem 12E

The equation of line is $2y=3x-16$

Explanation of Solution

Given: $\left(2,-5\right);2y=3x+10$

Formula Used:

Equation of line passing through a point and has a known slope is given as

  $y-y_1=m\left(x-x_1\right)$ , where

  $\begin{array}{l}m=slope\\ \left(x_1,y_1\right)=po\mathrm{int}\end{array}$

When two lines are parallel, then the slopes of lines are equal

Calculation:

Given the equation of line as follows:

  $\begin{array}{l}2y=3x+10\\ y=\frac{3}{2}x+5\end{array}$

Since the line is parallel to the above line, thus the slope of line is given as

  $m=m_1$

Thus, slope of line is calculated as

  $m=\frac{3}{2}$

Thus, equation of line is with slope $m=\frac{3}{2}$ and passing through point $\left(2,-5\right)$ calculated as follows:

  $y-y_1=m\left(x-x_1\right)$

Substituting the values in above equation:

  $\begin{array}{l}y-\left(-5\right)=\frac{3}{2}\left(x-2\right)\\ y+5=\frac{3}{2}x-3\\ y=\frac{3}{2}x-8\\ 2y=3x-16\end{array}$

Conclusion:

Hence, the equation of lineis $2y=3x-16$