Chapter 4.3, Problem 10E

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 10E

The equation of line is $y=-5x+7$

Explanation of Solution

Given: $\left(1,2\right);y=-5x+4$

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:

  $y=-5x+4$

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

  $m=-5$

Thus, equation of line is with slope $m=-5$ and passing through point $\left(1,2\right)$ calculated as follows:

  $y-y_1=m\left(x-x_1\right)$

Substituting the values in above equation:

  $\begin{array}{l}y-2=-5\left(x-1\right)\\ y-2=-5x+5\\ y=-5x+7\end{array}$

Conclusion:

Hence, the equation of lineis $y=-5x+7$