Question

1. write an equation in point - slope form to represent the table. then explain the meaning of the slope. time in minutes 3 5 7 9 apples picked 15 23 31 39

Explanation:

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(3,15)\) and \((x_2,y_2)=(5,23)\).
\(m=\frac{23 - 15}{5 - 3}=\frac{8}{2}=4\)

Step2: Use the point - slope form

The point - slope form is \(y - y_1=m(x - x_1)\). Using the point \((3,15)\) and \(m = 4\), we get \(y-15 = 4(x - 3)\)

Step3: Explain the slope

The slope \(m = 4\) means that for every 1 - minute increase in time, the number of apples picked increases by 4.

Answer:

The equation in point - slope form is \(y-15 = 4(x - 3)\). The slope of 4 means that the number of apples picked increases by 4 for each additional minute of time.