Which variable is something you can choose to change? Can you choose the temperature? Can you choose the velocity of the sound in air?
Independent Variable: Temperature Dependent Variable: Velocity of sound in air In Words: See solution. Equation: V = 35T + 331 Graph:
Practice makes perfect
The velocity of the sound in air is dependent on the temperature. This means that the velocity of the sound in air is the dependent variable and the temperature is the independent variable.
In Words
Let's look for a pattern of change in the given table.
As we can see in the table, every time the temperature rises 5 ^(∘) C, the velocity increases by 3 m/s. This might lead us to believe that the relationship is just three fifths of the temperature.
Velocity &? = 3/5 * Temperature
Unfortunately, by checking any of the points of the table, we can see that the pattern describe above does not work.
337 &≠ 3/5( 10) = 6 [0.7em]
340 &≠ 3/5( 15) = 9
The values are 331 less than what we need in each case. Therefore, the correct relationship between the temperature and the velocity of sound in air is as written below.
The velocity is equal to
three fifths of the temperature plus 331.
Equation for the Relationship
To describe the relation with an equation, let's translate our verbal description into algebraic terms.
The velocity is equal to
three fifthsof the temperature plus331
⇓ [0.7em]
V = 3/5 T + 331.
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. Notice that this function needs to be restricted to the 1^\text{st} and 2^\text{nd} quadrants because we cannot have a negative velocity but we can have negative temperatures.
