Question

the graph shows the relationship between time and the number of soda bottles a machine can make. use the points (5,160) and (7,224) to find the number of soda bottles the machine can make each minute.
the machine can make \\(\square\\) soda bottles each minute.

Explanation:

Step1: Recall slope formula

The number of bottles per minute is the slope of the line through the points \((x_1,y_1)=(5,160)\) and \((x_2,y_2)=(7,224)\). The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Substitute values

Substitute \(x_1 = 5\), \(y_1 = 160\), \(x_2 = 7\), \(y_2 = 224\) into the formula: \(m=\frac{224 - 160}{7 - 5}=\frac{64}{2}\).

Step3: Simplify

Simplify \(\frac{64}{2}=32\).

Answer:

32