Q 7 - Precalculus Enhanced with Graphing Utilities

Question

Determine the intercepts and graph each equation by hand by plotting points. Verify your results using a graphing utility. Label the intercepts on the graph. 

$2x-3y=6$.

Step-by-Step Solution

Answer

The intercepts of the given equation are :-

$\left(0,-2\right) and (3,0)$.

The required graph of given function is as following :-

We can plot the intercepts as following :-

Step 1. Given Information

We have given the following equation :-

$2x-3y=6$

We have to find intercepts and graph this function by hand by plotting points.

Also we have to verify our result by using graphing utility.

Also we have to label the intercepts over the graph.

Step 2. Determination of intercepts

The given equation is :-

$2x-3y=6$.

We know that where the function cut the x-axis or y-axis, that point is called intercept.

So to find intercept, put $x=0$ in the given equation, then we have :-

$$\begin{gathered} (2\times 0)-3y=6 \\ \Rightarrow 0-3y=6 \\ \Rightarrow -3y=6 \\ \Rightarrow y=-\frac{6}{3} \\ \Rightarrow y=-2 \end{gathered}$$

So the intercept is $\left(0,-2\right)$.

Now put $y=0$, then we have :-

$$\begin{gathered} 2x-(3\times 0)=6 \\ \Rightarrow 2x-0=6 \\ \Rightarrow 2x=6 \\ \Rightarrow x=\frac{6}{2} \\ \Rightarrow x=3 \end{gathered}$$

So the another intercept is $\left(3,0\right)$.

Step 3. Table of values

The give equation is :-

$2x-3y=6$.

Now we have to find table of points $\left(x,y\right)$, that satisfies the given equation $2x-3y=6$.

The required table of values is as following :-

Step 4. Plot the points

We find the following table in previous step :-

Now plot all these points on a graph then we have :-

Step 5. Draw graph

In previous step we plot all points on a graph.

Now join all these points, then we have the following graph of the given function :-

Step 6. Verify result using Graphing utility

Now draw the graph of the given function $2x-3y=6$, by using graphing utility, then we have the following graph :-

This graph is same as the hand made graph.

So our result is verified.

Step 7. Plot the intercepts

In the above hand made graph, we can plot the intercepts as following :-