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