Q. 85 - Precalculus Enhanced with Graphing Utilities

Question

Graph each equation by hand by plotting points. Verify your results using a graphing utility. 

$2x+3y=6$

Step-by-Step Solution

Answer

The required graph is 

Step 1. Given information.

Graph each equation by hand by plotting points. Verify your results using a graphing utility. 

$2x+3y=6$

Step 2. Create table of values.

We will rewrite the given equation to solve for y:

$$\begin{gathered} 2x+3y=6 \\ \frac{2}{3}x+\frac{3}{3}y=\frac{6}{3} \\ y=-\frac{2}{3}x+2 \end{gathered}$$

Start by creating a table of values, we will then use it to plot the points on the graph. select values of x and use the given equation to find the corresponding values of y. 

Step 3. Create the graph.

Plot the points from the table above and connect them with a smooth curve.

Step 4. Conclusion.

The required graph is