The function below shows the cost for Mrs. Franklin to go to a buffet with c of her grandchildren.
f(c) = 6.85 + 2.95c
a. What is the y-intercept, and what does it mean?
b. What is the slope, and what does it mean?
c. If Mrs. Franklin paid 18.65 for the buffet, how many of her grandchildren did she take to the buffet?
a. The y-intercept of the function is 6.85.
This means that even if Mrs. Franklin does not take any of her grandchildren to the buffet (c = 0), she still has to pay $6.85.
b. The slope of the function is 2.95.
This means that for each additional grandchild Mrs. Franklin takes to the buffet, the cost increases by $2.95.
c. To find the number of grandchildren Mrs. Franklin took to the buffet, we can set f(c) equal to the amount she paid, which is $18.65:
6.85 + 2.95c = 18.65
Subtracting 6.85 from both sides:
2.95c = 11.80
Dividing both sides by 2.95:
c = 4
Therefore, Mrs. Franklin took 4 of her grandchildren to the buffet.