Chapter 8.9, Problem 22SR

To determine

Use the slope- $y$ intercept form to draw a graph of $y=2x-3$

Answer to Problem 22SR

The graph of $y=2x-3$

  

Explanation of Solution

Given:

  $y=2x-3$

Concept Used:

The slope-intercept from is written as:

  $y=mx+b$

Where,

Slope: $m$

  $y-$ intercept: $b$

Calculation:

The given eq. is:

  $y=2x-3$..........(1)

That means:

  $\begin{array}{l}m=2\\ b=-3\end{array}$

So, the $y-$ intercept can be written as $\left(0,b\right)=\left(0,-3\right)$ . The $y-$ intercept is the point where the graph intersects with $y-$ axis.

Now draw the point $\left(0,b\right)=\left(0,-3\right)$ on graph:

  

Now, the slope is $m=\frac{y}{x}=\frac{2}{1}$ . Need to go up with $2units$ from the starting point $\left(0,-3\right)$ .

  

Now, go right side with $1unit$ to get the next point $\left(1,-1\right)$ .

  

Now, need to draw a line which is passing through these two points

  

The graph of $y=2x-3$ is passing through the points $\left(0,-3\right)$ and $\left(1,-1\right)$ .

Conclusion:

Hence, the graph of $y=2x-3$ is passing through the points $\left(0,-3\right)$ and $\left(1,-1\right)$ .