Question

for the following scenario, find the linear function that describes the relationship between the input value and the output value. then, determine whether the graph of the function is increasing, decreasing, or constant.
zeke sends about 61 texts a day. he has a limit of 400 texts per month in his data plan. the input is the number of days, and the output is the total number of texts remaining for the month.
the function can be represented as ( f(x) = ) enter your answer where ( x ) is the number of days.
the slope is enter your answer and the function is enter your answer (type \decreasing\, \increasing\, or \constant\)

Explanation:

Step1: Identify the slope

The slope is the rate of change. Zeke sends 61 texts a day. So the slope \(m = - 61\) (negative because the number of remaining texts is decreasing as days pass).

Step2: Identify the y - intercept

The y - intercept \(b\) is the initial value. The limit is 400 texts per month, so \(b = 400\).

Step3: Write the linear function

Using the slope - intercept form \(y=mx + b\), the function \(f(x)=-61x + 400\), where \(x\) is the number of days.

Step4: Determine if the function is increasing, decreasing, or constant

Since the slope \(m=-61<0\), as \(x\) (number of days) increases, \(f(x)\) (number of remaining texts) decreases.

Answer:

The function is \(f(x)=-61x + 400\), the slope is \(-61\), and the function is decreasing.