Chapter 4, Problem 30SGR

To determine

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

Answer to Problem 30SGR

An equation of line in slope- intercept form is $y=x+3$

Explanation of Solution

Given information:

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

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

  $y=x-3$

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

The slope of line $y=x-3$ is $m=1$ .

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

Therefore, the slope of required line is equal to slope of $y=x-3$ i.e. $m=1$

The required line passes through $\left(2,5\right)$ and having slope $1$ . Using point slope form of equation of line

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(2,5\right)\&m=1\\ y-5=1\left(x-2\right)\\ y-5=x-2\left(\text{Distributive property}\right)\\ \text{Add 5 on both sides}\\ y-5+5=x-2+5\\ y=x+3\end{array}$

Conclusion:

An equation of line in slope- intercept form is $y=x+3$