Question

proportional relationship and slope practice {hw}
a beverage company bottles their drinks at a constant rate. the table shows the number of drinks bottled for different lengths draws a graph of the number of drinks bottled after a certain number of minutes. what is the slope of the line?

the slope is

this means that the company bottles drinks per minute.

Explanation:

Step1: Recall the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points from the table. For example, \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(2,120)\).

Step2: Substitute values into the formula

Substitute \(x_1 = 0,y_1=0,x_2 = 2,y_2 = 120\) into \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We get \(m=\frac{120-0}{2 - 0}=\frac{120}{2}=60\). We can check with another pair of points, say \((x_1,y_1)=(5,300)\) and \((x_2,y_2)=(10,600)\). Then \(m=\frac{600 - 300}{10 - 5}=\frac{300}{5}=60\).

Answer:

The slope is \(60\). This means that the company bottles \(60\) drinks per minute.