Which variable is something you can choose to change? Can you choose the number of flights of stairs you climb? Can you choose the level of elevation?
Independent Variable:Flights of Stairs Climbed Dependent Variable: Elevation In Words: See solution. Equation: E=311 + 15n Graph:
Practice makes perfect
The level of elevation is dependent on the number of flights of stairs that have been climbed. This means that elevation is the dependent variable and number of flights of stairs climbed is the independent variable.
In Words
Before we can begin, we need to observe the changes in each row of the data.
Originally the elevation is 311 feet, and every time a flight of stairs is climbed, the elevation rises by 15 feet. We can express this verbally as the following.
The elevation is equal to the original 311feet
plus15 feet per flight of stairs climbed.
Equation for the Relationship
To write an equation that describes the relationship, we will translate the verbal expressions we created above into algebraic expressions. To do so, we will make a table
Verbal Expression
Algebraic Expression
Elevation (ft)
E
Starting elevation
311
Flights of stairs climbed
n
15ft per flight of stairs
15n
Starting elevation plus 15ft per flight of stairs
311+ 15n
The first expression and the last one represent the same quantity.
E= 311+ 15n
Therefore, this equation shows the relationship between E and n.
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 flights of stairs.
