Linear Equations and Graphing
Linear equations can be written in several different forms including slope-intercept form $(y=mx+b)$ and standard form $(ax+by=c)$. When writing equations to solve real life problem standard form is often more natural.
In this lesson we will solve a word problem by writing an equation in standard form and graphing it.
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Your turn:
At the Dragon Review theater tickets sell for $\$36$ for an adult and $\$24$ dollars for a student. The total income from ticket sales is $\$28,800$.
a. Write an equation in standard form to represent this situation.
b. What is the maximum number of adults that could have gone to the show?
c. What is the maximum number of students that could have gone to the show?
d. If you were to graph the solution, would this be a discrete graph (only whole numbers answers make sense) or continuous graph (answers can include decimals or fractions)?
Solution:
a. If we let x = the number of Adults
and let y = the number of Students
then the equation would be: $\color{blue}{36x+24y=28,800}$
b & c. When you use standard form the x and y-intercepts are easy to find.
$$
\begin{array}{c|c}
x & y\\
\hline
0 & 1,200\\
\hline
800 & 0\\
\hline
\end{array}
$$
So the maximum number of adults is when no students bought tickets $(y=0)$, or 800 adults; and the maximum number of students is when no adults bought tickets $(x=0)$, or 1,200 students.
d. This would be a discrete graph since you can not have a fraction of a person.
