Chapter 4.3, Problem 13PPS

To determine

To Write: An equation of line in slope intercept form that passes through point $\left(0,2\right)$ and is parallel to line $y=-5x+8$

Answer to Problem 13PPS

An equation of line in slope- intercept form is $y=-5x+2$

Explanation of Solution

Given information:

Line passes through point $\left(0,2\right)$ and is parallel to line $y=-5x+8$

Concept and Formula Used:

Slope intercept form $y=mx+c$ where $m$ is slope and $c$ is intercept.

Point slope form of a line: $y-y_1=m\left(x-x_1\right)$

Parallel lines: If lines are parallel then the slopes of lines are equal

Calculation:

The required line is parallel to

  $y=-5x+8$

Now, find the slope of given line by compairing it with $y=mx+c$ .

The slope of line $y=-5x+8$ is $-5$ .

Let the slope of required line be ‘m’. As the required line is parallel to $y=-5x+8$

Therefore, the slope of required line is equal to slope of $y=-5x+8$ i.e. $m=-5$

The required line passes through $\left(0,2\right)$ and having slope $-5$ . Using point slope form of equation of line

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(0,2\right)\&m=-5\\ y-\left(2\right)=-5\left(x-\left(0\right)\right)\\ y-2=-5x\left(\text{Distributive property}\right)\\ \text{Add 2 on both sides}\\ y-2+2=-5x+2\\ y=-5x+2\end{array}$

Conclusion:

An equation of line in slope- intercept form is $y=-5x+2$