Chapter 8.9, Problem 20SR

To determine

Use the slope- $y$ intercept form to draw a graph of $y=x+5$

Answer to Problem 20SR

The graph of equation $y=x+5$

  

Explanation of Solution

Given:

  $y=x+5$

Concept Used:

The slope-intercept from is written as:

  $y=mx+b$

Where,

Slope: $m$

  $y-$ intercept: $b$

Calculation:

The given eq. is:

  $y=x+5$..........(1)

That means:

  $\begin{array}{l}m=1\\ b=5\end{array}$

So, the $y-$ intercept can be written as $\left(0,b\right)=\left(0,5\right)$ . The $y-$ intercept is the point where the graph intersects with $y-$ axis.

Now draw the point $\left(0,b\right)=\left(0,5\right)$ on graph:

  

Now, the slope is $m=1$ . So, the first point to draw a line graph is $\left(0,5\right)$

Let take the value $x=3$ of then calculate the value of $y$

  $y=x+3=3+5=8$

So, the second point is $\left(3,8\right)$

Check the line which is passing through the two points $\left(0,5\right)$ and $\left(3,8\right)$

  

Conclusion:

Hence, the graph of $y=x+5$ is passing through the points $\left(0,5\right)$ and $\left(3,8\right)$