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Answer :
To understand what the slope means in the context of this taxi ride cost function, we start by looking at the given equation:
[tex]\[ q(x) = 3x + 2.00 \][/tex]
Here, [tex]\( q(x) \)[/tex] represents the total cost of the taxi ride in dollars, and [tex]\( x \)[/tex] represents the number of minutes of the ride.
The structure of this equation is similar to a linear function, which can be expressed in the form:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
1. Identify the Slope: In our taxi ride equation, the term [tex]\( 3x \)[/tex] indicates that the slope, [tex]\( m \)[/tex], is 3. The slope represents how much the total cost changes with each additional minute of the ride.
2. Interpret the Slope: Since the slope is 3, this means that for every additional minute the taxi ride lasts, the cost increases by [tex]$3.00. Thus, the cost per minute of the taxi ride is $[/tex]3.00.
3. Understanding [tex]\( b \)[/tex] (the Y-Intercept): The [tex]\( b \)[/tex] value in the equation is [tex]$2.00. This is the starting cost or initial charge for the ride, even before any time has passed.
Based on this interpretation:
- The correct interpretation of the slope here is:
C. The rate of change of the cost of the taxi ride is $[/tex]3.00 per minute.
This means that for each minute spent in the taxi, the cost increases by $3.00.
[tex]\[ q(x) = 3x + 2.00 \][/tex]
Here, [tex]\( q(x) \)[/tex] represents the total cost of the taxi ride in dollars, and [tex]\( x \)[/tex] represents the number of minutes of the ride.
The structure of this equation is similar to a linear function, which can be expressed in the form:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
1. Identify the Slope: In our taxi ride equation, the term [tex]\( 3x \)[/tex] indicates that the slope, [tex]\( m \)[/tex], is 3. The slope represents how much the total cost changes with each additional minute of the ride.
2. Interpret the Slope: Since the slope is 3, this means that for every additional minute the taxi ride lasts, the cost increases by [tex]$3.00. Thus, the cost per minute of the taxi ride is $[/tex]3.00.
3. Understanding [tex]\( b \)[/tex] (the Y-Intercept): The [tex]\( b \)[/tex] value in the equation is [tex]$2.00. This is the starting cost or initial charge for the ride, even before any time has passed.
Based on this interpretation:
- The correct interpretation of the slope here is:
C. The rate of change of the cost of the taxi ride is $[/tex]3.00 per minute.
This means that for each minute spent in the taxi, the cost increases by $3.00.
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