Khadija's cab company charges a one-time pickup fee for every ride, as well as a charge for each mile traveled. The equation y = 3x + 5 represents what Khadija's company charges. F... Khadija's cab company charges a one-time pickup fee for every ride, as well as a charge for each mile traveled. The equation y = 3x + 5 represents what Khadija's company charges. Find the rate of change.

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Understand the Problem

The question is asking to find the rate of change represented by the equation y = 3x + 5, where y is the total charge and x is the number of miles traveled. The rate of change in this context refers to the charge per mile.

Answer

$3$ per mile.
Answer for screen readers

The rate of change is $3$ per mile.

Steps to Solve

  1. Identify the rate of change from the equation

The equation given is $y = 3x + 5$. Here, $y$ represents the total charge, and $x$ represents the number of miles traveled. The slope of the equation indicates the rate of change.

  1. Extract the slope

In the equation $y = mx + b$, $m$ represents the slope. In our equation, $m = 3$.

  1. Interpret the slope in context

The slope of 3 means that for each mile traveled (increase in $x$), the total charge ($y$) increases by $3. Therefore, the rate of change (the charge per mile) is $3$.

The rate of change is $3$ per mile.

More Information

In this context, the rate of change indicates how much the charge increases for each mile traveled. If someone rode 5 miles, the additional charge would be $3 \times 5 = 15$ dollars, plus any fixed fees that may apply.

Tips

  • Confusing the total charge with the rate of change. Remember, the rate of change refers specifically to the coefficient of $x$ in the equation.
  • Overlooking the fixed cost represented by the constant term. The constant term ($5$) does not affect the rate of change.

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