The cost y (in dollars) to provide food for guests at a dinner party is proportional to the number x of guests attending the party. IT costs $30 to provide food for 4 guests.
a. Write an equation that represents the situation.
b. Interpret the slope.
c. How much does it cost to provide food for 10 guests?
Please give examples of the ordered pairs. Preferably 2, 4, and 0 for x
I don't know the answer tell me please
goodjob
a. To write an equation that represents the situation, we know that the cost y is proportional to the number x of guests attending the party. We are given that it costs $30 to provide food for 4 guests. Let's define the constant of proportionality as k.
The equation that represents the situation is: y = kx.
To find the value of k, we can use the given information. When x = 4, y = 30. Plugging these values into the equation, we get: 30 = 4k. Solving for k, we find k = 7.5.
Therefore, the equation that represents the situation is: y = 7.5x.
b. The slope of the equation represents the rate at which the cost changes with respect to the number of guests. In this case, the slope is 7.5.
Interpreting the slope, for every additional guest, the cost of providing food increases by $7.50. This means that for every unit increase in the number of guests attending the party, the cost increases by $7.50.
c. To find how much it costs to provide food for 10 guests, we can plug in the value of x = 10 into the equation y = 7.5x.
y = 7.5 * 10 = 75.
Therefore, it would cost $75 to provide food for 10 guests.
For the ordered pairs:
When x = 2, y = 7.5 * 2 = 15. So, the ordered pair is (2, 15).
When x = 4, y = 7.5 * 4 = 30. So, the ordered pair is (4, 30).
When x = 0, y = 7.5 * 0 = 0. So, the ordered pair is (0, 0).
a. $30/4gueest = $7.5 per guest
Y = 7.5x
b. Slope = 7.5
c. Y = 7.5x = 7.5 * 10 = $75
(x, y) = (10,75).
(2,15), (4,30), (0,0).