Let's solve the problem step-by-step.
1. Understanding the function:
The cost function for a taxi ride is given by [tex]\( c(x) = 3x + 2.00 \)[/tex]. Here, [tex]\( x \)[/tex] represents the number of minutes, and [tex]\( c(x) \)[/tex] is the cost in dollars.
2. Identifying the components:
- The y-intercept (where [tex]\( x = 0 \)[/tex]) is the constant term in the equation, which here is 2.00. This means that even if the ride duration is 0 minutes, there is a base fare of [tex]$2.00.
- The slope of the line, represented by the coefficient of \( x \), is 3. This means that for each additional minute, the cost increases by $[/tex]3.00.
3. Plotting the graph:
- Step 1: Begin by plotting the y-intercept. At [tex]\( x = 0 \)[/tex], the cost [tex]\( c(x) = 2.00 \)[/tex]. Plot this point on the coordinate plane as (0, 2.00).
- Step 2: Use the slope to find another point. The slope is 3, indicating that for each increase of 1 minute in [tex]\( x \)[/tex], the cost [tex]\( c(x) \)[/tex] increases by 3 dollars. Thus, if [tex]\( x = 1 \)[/tex], then [tex]\( c(1) = 3(1) + 2.00 = 5.00 \)[/tex]. Plot this point (1, 5.00).
- Step 3: Connect these two points with a straight line. The line will extend through these points, showing the linear relationship between minutes and cost.
4. Labels:
- The horizontal axis (x-axis) should be labeled “Minutes” because it represents the number of minutes, [tex]\( x \)[/tex].
- The vertical axis (y-axis) should be labeled “Cost in dollars” because it represents the cost, [tex]\( c(x) \)[/tex].
5. Determining the correct answer:
- You should look at the graph options provided. The correct graph should have:
- The y-intercept at [tex]\( (0, 2.00) \)[/tex].
- A slope of 3, meaning the line rises 3 units up for every 1 unit it moves to the right.
- Properly labeled axes with "Minutes" on the x-axis and "Cost in dollars" on the y-axis.
- A linear form (straight line).
Assuming “A” is the answer choice that matches these criteria, then A would be the correct graph. Make sure to cross-check your plotted graph with the given answer choices to ensure accuracy.
