Question

1. niko drinks his shake at a constant rate. after drinking the shake for 3 minutes, there are 14 oz of shake left in the cup. after 9 minutes, the cup is empty.

a. graph the relationship between the time in minutes, and the ounces of shake left in his cup.
b. write an equation for s, the ounces of shake left in the cup, after t minutes.
c. identify the x and y intercepts and explain their meaning in the context of the problem.

Explanation:

Step1: Find the slope

We have two points \((t_1,s_1)=(3,14)\) and \((t_2,s_2)=(9,0)\).
The slope \(m=\frac{s_2 - s_1}{t_2 - t_1}=\frac{0 - 14}{9 - 3}=\frac{-14}{6}=-\frac{7}{3}\)

Step2: Use the point - slope form

Using the point - slope form \(s - s_1=m(t - t_1)\), with \(m =-\frac{7}{3}\) and \((t_1,s_1)=(9,0)\)
\(s-0=-\frac{7}{3}(t - 9)\)
\(s=-\frac{7}{3}t+21\)

Step3: Find the \(y\) - intercept

When \(t = 0\), \(s=-\frac{7}{3}(0)+21=21\)

Step4: Find the \(x\) - intercept

We already know from the problem that when \(s = 0\), \(t = 9\)

Answer:

b. The equation is \(s=-\frac{7}{3}t + 21\)
c. The \(y\) - intercept is \((0,21)\), which means that initially (at \(t = 0\) minutes), there are \(21\) ounces of shake in the cup. The \(x\) - intercept is \((9,0)\), which means that after \(9\) minutes (\(t=9\)), there are \(0\) ounces of shake left in the cup (the cup is empty).