35.1: Tables, Equations, and Graphs, Oh My!
Lesson
Let's explore some equations from real-world situations.
Exercise \(\PageIndex{1}\): Matching Equations and Tables
Match each equation with a table that represents the same relationship. Be prepared to explain your reasoning.
\(\begin{array}{lllllll}{S-2=T}&{\qquad}&{G=J+13}&{\qquad}&{P=I-47.50}&{\qquad}&{C+273.15=K}\\{e=6s}&{\qquad}&{m=8.96V}&{\qquad}&{y=\frac{1}{12}x}&{\qquad}&{t=\frac{d}{2.5}}\\{g=28.35z}&{}&{}&{}&{}&{}&{}\end{array}\)
Table 1:
| independent variable | dependent variable |
|---|---|
| \(20\) | \(8\) |
| \(58.85\) | \(23.54\) |
| \(804\) | \(321.6\) |
Table 2:
| independent variable | dependent variable |
|---|---|
| \(5\) | \(18\) |
| \(36\) | \(49\) |
| \(75\) | \(88\) |
Table 3:
| independent variable | dependent variable |
|---|---|
| \(2.5\) | \(22.4\) |
| \(20\) | \(179.2\) |
| \(75\) | \(672\) |
Table 4:
| independent variable | dependent variable |
|---|---|
| \(20\) | \(1\frac{2}{3}\) |
| \(36\) | \(3\) |
| \(804\) | \(67\) |
Table 5:
| independent variable | dependent variable |
|---|---|
| \(58.85\) | \(11.35\) |
| \(175.5\) | \(128\) |
| \(804\) | \(756.6\) |
Table 6:
| independent variable | dependent variable |
|---|---|
| \(2.5\) | \(275.65\) |
| \(20\) | \(293.15\) |
| \(58.85\) | \(332\) |
Table 7:
| independent variable | dependent variable |
|---|---|
| \(5\) | \(3\) |
| \(20\) | \(18\) |
| \(36\) | \(34\) |
Table 8:
| independent variable | dependent variable |
|---|---|
| \(2.6\) | \(73.71\) |
| \(20\) | \(567\) |
| \(36\) | \(1,020,6\) |
Table 9:
| independent variable | dependent variable |
|---|---|
| \(2.6\) | \(15.6\) |
| \(36\) | \(216\) |
| \(58.85\) | \(353.1\) |
Exercise \(\PageIndex{2}\): Getting to Know an Equation
The equations in the previous activity represent situations.
- \(S-2=T\) where \(S\) is the number of sides on a polygon and \(T\) is the number of triangles you can draw inside it (from one vertex to the others, without overlapping)
- \(G=J+13\) where \(G\) is a day in the Gregorian calendar and \(J\) is the same day in the Julian calendar
- \(P=I-47.50\) where \(I\) is the amount of income and \(P\) is the profit after $47.50 in expenses
- \(C+273.15=K\) where \(C\) is a temperature in degrees Celsius and \(K\) is the same temperature in Kelvin
- \(e=6s\) where \(e\) is the total edge length of a regular tetrahedron and \(s\) is the length of one side
- \(m=8.96V\) where \(V\) is the volume of a piece of copper and \(m\) is its mass
- \(y=\frac{1}{12}x\) where \(x\) is the number of eggs and \(y\) is how many dozens that makes
- \(t=\frac{d}{2.5}\) where \(t\) is the amount of time it takes in seconds to jog a distance of \(d\) meters at a constant speed of 2.5 meters per second
- \(g=28.35z\) where \(g\) is the mass in grams and \(z\) is the same amount in ounces
Your teacher will assign you one of these equations to examine more closely.
- Rewrite your equation using words. Use words like product, sum, difference, quotient, and term.
-
In the previous activity, you matched equations and tables. Copy the values from the table that matched your assigned equation into the first 3 rows of this table. Make sure to label what each column represents.
independent variable:
________________________dependent variable:
________________________\(60\) \(300\) Table \(\PageIndex{10}\) - Select one of the first 3 rows of the table and explain what those values mean in this situation.
- Use your equation to find the values that complete the last 2 rows of the table. Explain your reasoning.
- On graph paper, create a graph that represents this relationship. Make sure to label your axes.
Exercise \(\PageIndex{3}\): Sharing Your Equation with Others
Create a visual display of your assigned relationships that includes:
- your equation along with an explanation of each variable
- a verbal description of the relationship
- your table
- your graph
If you have time, research more about your relationship and add more details or illustrations to help explain the situation.