Question

a health club charges a one - time sign - up fee and a monthly membership fee. the equation y = 55x + 35 represents what the health club charges. find the rate of change.

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept.

Step2: Identify \(m\) in the given equation

In the equation \(y = 55x+35\), comparing it with \(y = mx + b\), we can see that \(m = 55\). The rate of change in a linear equation representing a real - world situation like this (where \(x\) is the number of months and \(y\) is the total cost) is the coefficient of \(x\), which represents the monthly membership fee (the rate at which the total cost changes with respect to the number of months).

Answer:

The rate of change is 55.