Which variable is something you can choose to change? Can you choose the number of ounces of paint you need per chair? Can you choose how many chairs to paint?
Independent Variable: Number of chairs painted Dependent Variable: Amount of paint left In words: See solution. Equation: L=128-30p Graph:
Practice makes perfect
The number of ounces of paint left is dependent on the number of chairs that have been painted. This means that ounces of paint left is the dependent variable and number of chaired painted is the independent variable.
In Words
Before we can begin, we need to observe the changes in each row of the data.
Originally the paint can contained 128 ounces of paint, and every time a chair is painted, the amount of paint remaining in the can is reduced by 30 ounces. We can express this relationship with a sentence.
The amount of paint left is equal to the original128ounces of paint minus30ounces per chair painted.
Equation for the Relationship
To write an equation that describes the relationship, we will translate the verbal expressions we created above into algebraic expressions.
Let's make a table for this purpose.
Verbal Expression
Algebraic Expression
Amount of paint left
L
Original amount of paint (oz)
128
Number of painted chairs
p
30 ounces per chair painted
30p
Original amount of paint minus 30 ounces per chair painted
128- 30p
The first expression and the last one represent the same quantity.
L= 128- 30p
Therefore, this equation shows the relationship between L and p.
Graph of the Relationship
To show the data graphically, begin by plotting the points on a coordinate plane.
We can then show the graph of the function by connecting those points with a straight line. Note, the function is restricted to the 1^\text{st} Quadrant because we cannot have a negative number of chairs and we cannot continue painting after our paint has run out.
