Question

section 5.2 slope and y - intercepts
objective 1 - interpret slopes as rates
objective 2 - interpret y - intercepts as initial values
objective 1 - interpret slopes as rates
guided practice activity #3 - slopes
this worksheet asks you to interpret slopes as rates using the sentence template:
the <output> is changing by <slope> <y - units> per <x - units>.

1. monthly cell phone bill:

cost of 5c plan with the monthly fee
a. interpret the slope of the equation in real world terms.

Explanation:

Step1: Identify the equation form

The equation given is \( y = 0.05x + 20 \), which is in the slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, the slope \( m = 0.05 \).

Step2: Determine the variables

In the context of the cell phone bill problem, the x - axis represents the number of minutes (the input variable) and the y - axis represents the cost in dollars (the output variable).

Step3: Interpret the slope

The slope represents the rate of change of the output variable (cost) with respect to the input variable (minutes). Since the slope \( m = 0.05 \) (or 5 cents, because \( 0.05\) dollars \(= 5\) cents) and the units of x are minutes and the units of y are dollars, we can interpret the slope as follows: The cost (in dollars) of the cell phone bill is changing by \( 0.05 \) dollars (or 5 cents) per minute. Using the given sentence template: The cost (output) is changing by \( 0.05 \) dollars (slope) per minute (x - units).

Answer:

The cost of the cell phone bill is changing by \( \$0.05 \) (or 5 cents) per minute. In the context of the sentence template: The cost is changing by \( 0.05 \) dollars per minute.