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. It represents the cost for Mrs. Franklin when she does not bring any of her grandchildren to the buffet. In other words, it is the fixed cost that Mrs. Franklin has to pay regardless of the number of her grandchildren.
b. The slope of the function is 2.95. It represents the additional cost that Mrs. Franklin has to pay for each grandchild she brings to the buffet. In other words, for each additional grandchild, the cost increases by 2.95 dollars.
c. To find the number of grandchildren Mrs. Franklin took to the buffet, we can solve the equation 18.65 = 6.85 + 2.95c for c. Rearranging the equation, we have 2.95c = 18.65 - 6.85, which simplifies to 2.95c = 11.8. Dividing both sides of the equation by 2.95, we get c = 11.8/2.95 = 4. Therefore, Mrs. Franklin took 4 of her grandchildren to the buffet.