Q. 87 - Precalculus Enhanced with Graphing Utilities

Question

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

$9x^2+4y=36$

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.

$9x^2+4y=36$

Step 2. Create table of values.

We will rewrite the given equation to solve for y: 

$$\begin{gathered} 9x^2+4y=36 \\ \frac{9}{4}{x}^2+\frac{4}{4}y=\frac{36}{4} \\ y=-\frac{9}{4}{x}^2+9 \end{gathered}$$

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