AThe cost y is $ 30 when the number of guests x is 4.
BThe slope of a graph describes the change in y when x increases by 1.
CFind the value of y that corresponds to x=10.
Ay=7.5x
BThe cost is $ 7.50 per guest.
C$ 75
Practice makes perfect
We want to write an equation that represents the cost y in dollars to provide food for a dinner party with x guests. We know that the cost y is proportional to the number of attending guests. A proportional relationship is represented by the following general equation, where m is the constant of proportionality.
y=mxWe want to find the value of m for our situation. We know that the cost is $ 30 when there are 4 guests. This means that y=30 when x=4. Therefore, we can substitute 30 for y and 4 for x in the general equation to determine our value of m.
Finally, we replace m with 7.5 in the general equation.
y=mx ⇒ y= 7.5x
We found the equation for our situation in Part A.
y=7.5x
We see that the constant of proportionality is 7.5. This represents the slope of the graph of the equation. Let's plot the graph and mark the slope. Remember, proportional relationships always pass through the origin so we know that we can start the graph at (0,0).
We see that when the value of x increases by 1, the value of y increases by 7.5. In our context, this means that the cost increases by $ 7.50 when the number of people attending the dinner party increases by 1. In other words, the cost of providing food for the dinner party is $ 7.50 per guest.
In this part, we want to calculate the cost of providing food for 10 guests. Previously, we found the equation that represents this situation.
y=7.5x
We can substitute 10 for the number of attending guests x in the equation to get the corresponding value of the cost y.
