Chapter 4.3, Problem 10E

To determine

ToWrite: an equation of the line that passes through the given point and is parallel to the given line.

Answer to Problem 10E

Equation ofline is $y=-5x+7$ .

Explanation of Solution

Given information:The given points and parallel line is $(1,2);y=-5x+4$ respectively.

Calculation:The slope of parallel line is:

Compare with

  $\begin{array}{l}y=mx+c\\ y=-5x+4\\ \mathrm{we}\mathrm{get}\\ m=-5\end{array}$

Slope of line $=$ slope of parallel line.

So the parallel line that passes through $(1,2)$ also has slope of $-5$ .

Use slope intercept form to find the y intercept of the parallel line.

  $\begin{array}{l}y=mx+b\\ 2=-5(1)+b\\ 2=-5+b\\ 2+5=b\\ 7=b\end{array}$

Using $m=-5\mathrm{and}b=7$ equation of line is $y=-5x+7$ .

Therefore,equation of line is $y=-5x+7$ .