Equations with Independent and Dependent Variables
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Common Core Standard: Use variables to represent two quantities in a real-world problem that change in
relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in
terms of the other quantity, thought of as the independent variable. Analyze the relationship between the
dependent and independent variables using graphs and tables, and relate these to the equation.
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Dependent variable – is a variable that changes because of the other variable or depends on the other variable
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Independent variable –is a variable that is not impacted by other variables
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Dependent and independent variables are very common in the real world
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Example: Most coaches will say that the longer a player practices a sport the better the player will be at the sport.
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The dependent variable is the player’s ability, as it relies on the length of a practice
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The independent variable is the number of hours the player practices, because the player’s ability does not
impact the amount of time the player practices
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Example: Kenneth’s family is going a trip. They travel an average of 65 mph. using this information complete the
table below to determine the distance the family travels at various hours.
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To determine the miles traveled, first determine how the two variables are related
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The two variables are the time and the distance
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To determine the distance, multiply the time by the speed, 65 mph
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Remember the unit rate 65 miles per hour, means 65 miles traveled in 1 hour
Now, multiply the time by 65 to determine each distance
Time (Hours)
Distance
(Miles)
1
65
2
130
3
195
4
260
5
325
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Example: Using the table from the previous example, determine an equation for the two variables. Also,
determine which variable is independent and which is dependent
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Dependent variable is the distance, because it is directly related to the time
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The more the time increases, the distance increases
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The time impacts the distance
Independent variable is the time, because the distance does not impact it
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o
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The distance cannot increase without the time increases
For the equation, determine how the variables are related
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These variables are related by multiplying the time by the speed, 65mph
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The time and the distance are variables, because we don’t know exactly what they equal
The equation: d = 65t
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Let d represent the distance
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Let t represent the time
Example: John is selling granola bars as part of a fundraiser. Each bar sells for $0.50. The granola bars are
given to John in a box, which contain 10 bars per box. John and his friends sell quite a few boxes. Below is a
table that shows how much money was made from the boxes sold. Determine how much money was made
for the boxes sold. Then, determine which variable is the dependent and which is independent and
determine an equation.
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Each box will earn $0.50 ● 10, because there are 10 bars in each box
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So each box will earn $5
Boxes Sold
Money
Earned
1
5
2
10
5
25
10
50
20
100
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The dependent variable is the money raised, because the number of boxes sold earns the money
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The independent variable is the number of boxes sold
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NOTE: You could flip these, but you need to explain why
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Before we can determine an equation, we must specify the variables
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b = number of boxes sold
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m = money earned
To determine the equation, we must know how the boxes and money are related
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For each box sold, the money earned was $5
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This means that if you multiply the number of boxes by $5, you will determine the amount of
money made
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m = $5b, is the equation relating this situation
Note: It is possible to determine a generic equation or an equation that always works in relation to dependent
and independent variables
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This you need to determine on your own 