Lesson 19
Tables, Equations, and Graphs, Oh My!
 Let’s explore some equations from realworld situations.
19.1: Matching Equations and Tables
Match each equation with a table that represents the same relationship. Be prepared to explain your reasoning.
\(S  2 = T\)
\(G = J + 13\)
\(P = I  47.50\)
\(C + 273.15 = K\)
\(e = 6s\)
\(m = 8.96V\)
\(y = \frac{1}{12}x\)
\(t = \frac{d}{2.5}\)
\(g = 28.35z\)
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  \(1\frac23\) 
36  3 
804  67 
Table 5:
independent variable 
dependent variable 

58.85  11.35 
175.5  128 
804  756.5 
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 
19.2: 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  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.
19.3: 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.