We would like to find the points on the graph of \(~~y = \dfrac{3}{x -2}~~\) that have \(y\)-coordinate equal to \(4\text{.}\) We graph the two functions
\begin{equation*}
\begin{aligned}[t]
Y_1 \amp = 3/(X - 2) \\
Y_2 \amp = 4
\end{aligned}
\end{equation*}
in the window
\begin{equation*}
\begin{aligned}[t]
\text{Xmin} \amp = -9.4 \amp\amp \text{Xmax} = 9.4\\
\text{Ymin} \amp = -10 \amp\amp \text{Ymax} = 10
\end{aligned}
\end{equation*}
The point where the two graphs intersect locates the solution of the equation. If we trace along the graph of \(Y_1\text{,}\) the closest we can get to the intersection point is \((2.8, 3.75)\text{,}\) as shown in figure (a). We get a better approximation using the intersect feature.
Use the arrow keys to position the Trace bug as close to the intersection point as you can. Then press 2nd TRACE to see the Calculate menu. Press \(5\) for intersect; then respond to each of the calculator’s questions, First curve?, Second curve?, and Guess? by pressing ENTER. The calculator will then display the intersection point, \(x = 2.75\text{,}\) \(y = 4\text{,}\) as shown in figure (b). The solution of the original equation is \(x = 2.75\text{.}\)