Alright, Leslie, let's tackle this problem step by step.
### Part a: Writing the Equation
In this problem, "y = mx + b" is the form of the linear equation you need, where:
- [tex]\( y \)[/tex] represents the total cost in dollars.
- [tex]\( x \)[/tex] represents the volume of gas purchased in gallons.
- [tex]\( m \)[/tex] is the slope of the line, which in this context is the price per gallon of gas.
- [tex]\( b \)[/tex] is the y-intercept, which is the fixed cost. In this case, since there is no initial fixed cost, [tex]\( b = 0 \)[/tex].
Given that the price per gallon ([tex]\( m \)[/tex]) is [tex]$2.40, the equation can be written as:
\[ y = 2.40x + 0 \]
Simplifying, the equation is:
\[ y = 2.40x \]
### Part b: Drawing the Graph
To graph this equation, we'll follow these steps:
1. Label the Axes:
- The x-axis will represent the volume of gas in gallons.
- The y-axis will represent the total cost in dollars.
2. Plot Points:
- To plot the graph, we can choose various values of \( x \) (gallons of gas) and compute the corresponding \( y \) values (total cost).
- For example, let’s choose points: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 gallons.
3. Calculate and Plot:
- If \( x = 0 \) gallons, \( y = 2.40 \times 0 = 0 \) dollars.
- If \( x = 1 \) gallon, \( y = 2.40 \times 1 = 2.40 \) dollars.
- If \( x = 2 \) gallons, \( y = 2.40 \times 2 = 4.80 \) dollars.
- And so forth up to 10 gallons.
Now, let's represent these points on a graph.
Cost vs Volume Graph:
On the x-axis (Volume of gas in gallons) and y-axis (Cost in dollars):
- (0, 0)
- (1, 2.40)
- (2, 4.80)
- (3, 7.20)
- (4, 9.60)
- (5, 12.00)
- (6, 14.40)
- (7, 16.80)
- (8, 19.20)
- (9, 21.60)
- (10, 24.00)
Line Plot:
You will draw a straight line passing through these points, starting from the origin (0,0) and extending through these calculated points.
### Summary of Graph Features:
1. The line will start at the origin (0,0).
2. It will have a constant upward slope.
3. The slope (rate of increase) is $[/tex]2.40 per gallon.
By following these steps, you now have both the equation and the graph representing the relationship between the cost of gas and the volume purchased at the gas station.
