Chapter 8, Problem 38SGR

To determine

To plot: the given equation using the slope and y-intercept.

Answer to Problem 38SGR

The graph of $y=\frac{3}{2}x-3$ is

  

Explanation of Solution

Given:

  $y=\frac{3}{2}x-3$

Calculation:

Consider the equation: $y=\frac{3}{2}x-3$

Step 1: Find the slope and y intercept

The general form of equation of line in slope intercept form is:

  $y=mx+b$

Here, m represents slope intercept andb stands for y intercept.

Hence, the equation $y=\frac{3}{2}x+\left(-3\right)$ is written in the form of $y=mx+b$

So, the slope is $\frac{3}{2}$ andthe y interceptis -3.

Step 2: Graph the y intercept point at (0, -3)

  

Step 3: Use the value of slope to locate the second point.

As, slope is change iny with respect to change in x

Since, slope is $\frac{3}{2}$

Move 3 units up and 2 unit’s right from y intercept to get another point.

Step 4: Draw a line through the two points.

  

Hence, the graph of $y=\frac{3}{2}x-3$ is shown above.

Conclusion:

Therefore, the graph for the given equation is plotted.