Final answer:
The slope represents the cost per person, and the y-intercept represents the initial cost when no one attends the dinner party. The cost for a dinner party of 20 people is $615, and for a charge of $265, 6 people attended the dinner party.
Step-by-step explanation:
a. Slope:
The slope represents the rate of change in the function. In this situation, the slope represents the cost per person. To find the slope, we can use the slope formula: (change in y) / (change in x).
Using the given information, we can calculate the slope:
Slope = (690 - 540) / (23 - 17) = 150 / 6 = 25
Therefore, the slope in this situation is $25 per person.
b. Y-Intercept:
The y-intercept represents the initial value or fixed cost in the function. In this situation, the y-intercept represents the cost when there are no people attending the dinner party.
Using the given information, we can determine the y-intercept as follows:
When x = 0, y = 540 - (25 * 17) = 540 - 425 = 115
Therefore, the y-intercept in this situation is $115.
c. Cost for a Dinner Party of 20 People:
To find the cost for a dinner party of 20 people, we can use the equation of the line. Substituting x = 20 into the equation,
y = 115 + (25 * 20) = 115 + 500 = 615
Therefore, the cost for a dinner party of 20 people is $615.
d. Number of People attended the Dinner Party for a Charge of $265:
To find the number of people who attended the dinner party for a charge of $265, we can use the equation of the line. Rearranging the equation to solve for x,
265 = 115 + (25 * x)
150 = 25 * x
x = 6
Therefore, the number of people attended the dinner party for a charge of $265 is 6.