Chapter 4, Problem 12PT

To determine

To Write: An equation of line in slope intercept form that passes through point $\left(-5,1\right)$ and is parallel to line $y=-3x+2$

Answer to Problem 12PT

An equation of line is $y=-3x+16$

Explanation of Solution

Given information:

Line passes through point $\left(-5,1\right)$ and is parallel to line $y=-3x+2$

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

  $y=-3x+2$

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

The slope of line $y=-3x+2$ is $-3$ .

Let the slope of required line be ‘m’. As the required line is parallel to $y=-3x+2$

Therefore, the slope of required line is equal to slope of $y=-3x+2$ i.e. $m=-3$

The required line passes through $\left(-5,1\right)$ and having slope $-3$ . Using point slope form of equation of line

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(-5,1\right)\&m=-3\\ y-\left(1\right)=-3\left(x-\left(-5\right)\right)\\ y-\left(1\right)=-3\left(x+5\right)\\ y-1=-3x+15\left(\text{Distributive property}\right)\\ \text{Add 1 on both sides}\\ y-1+1=-3x+15+1\\ y=-3x+16\end{array}$

Conclusion:

An equation of line is $y=-3x+16$