Chapter 4, Problem 37SGR

To determine

To Write: An equation of line in slope intercept form that passes through point $\left(3,0\right)$ and is parallel to line $y=-\frac{1}{2}x$

Answer to Problem 37SGR

An equation of line in slope- intercept form is $y=-\frac{1}{2}x-\frac{3}{2}$

Explanation of Solution

Given information:

Line passes through point $\left(3,0\right)$ and is parallel to line $y=-\frac{1}{2}x$

Concept and Formula Used:

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

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

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

Calculation:

The required line is parallel to

  $y=-\frac{1}{2}x$

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

The slope of line $y=-\frac{1}{2}x$ is $m=-\frac{1}{2}$ .

Let the slope of required line be ‘m’. As the required line is parallel to $y=-\frac{1}{2}x$

Therefore, the slope of required line is equal to slope of $y=-\frac{1}{2}x$ i.e. $m=-\frac{1}{2}$

The required line passes through $\left(3,0\right)$ and having slope $-\frac{1}{2}$ . Using point slope form of equation of line

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(3,0\right)\&m=-\frac{1}{2}\\ y-0=-\frac{1}{2}\left(x-3\right)\\ y=-\frac{1}{2}x-\frac{3}{2}\left(\text{Distributive property}\right)\end{array}$

Conclusion:

An equation of line in slope- intercept form is $y=-\frac{1}{2}x-\frac{3}{2}$