Question
Will bought 4 slices of pizza for $6.00.
Let x represent the number of slices of pizza purchased, and let y represent the total cost.
Graph the line that represents the proportional relationship.
Let x represent the number of slices of pizza purchased, and let y represent the total cost.
Graph the line that represents the proportional relationship.
Answers
GPT-4o mini
To represent the relationship between the number of slices of pizza (x) and the total cost (y) as a proportional relationship, you start with the information provided:
Will bought 4 slices of pizza for $6.00. This gives us a ratio of slices to cost:
- \( x = 4 \) (slices)
- \( y = 6 \) (dollars)
### Finding the Unit Rate
To understand the cost per slice, we can calculate the unit rate:
\[
\text{Cost per slice} = \frac{y}{x} = \frac{6}{4} = 1.5
\]
This means each slice of pizza costs $1.50.
### Equation of the Line
In the context of the linear relationship, the equation can be expressed as:
\[
y = mx
\]
where \( m \) is the slope (cost per slice).
Substituting the value we found:
\[
y = 1.5x
\]
### Graphing the Line
To graph this line, we need to plot points based on the equation \( y = 1.5x \).
#### Example Points
1. If \( x = 0 \), then \( y = 1.5(0) = 0 \) → Point (0, 0)
2. If \( x = 2 \), then \( y = 1.5(2) = 3 \) → Point (2, 3)
3. If \( x = 4 \), then \( y = 1.5(4) = 6 \) → Point (4, 6)
4. If \( x = 6 \), then \( y = 1.5(6) = 9 \) → Point (6, 9)
Now you can plot these points on a Cartesian coordinate system.
### Plotting the Graph
- On the x-axis, you would place the number of slices.
- On the y-axis, you would place the total cost in dollars.
- Use the points (0, 0), (2, 3), (4, 6), and (6, 9) to draw the line.
### Final Result
The line will be straight, starting at the origin (0, 0) and rising with a slope of 1.5. This line represents the proportional relationship between the number of pizza slices purchased and the total cost. Each point on the line corresponds to the cost of \( x \) slices of pizza, with the relationship defined by the equation \( y = 1.5x \).
Will bought 4 slices of pizza for $6.00. This gives us a ratio of slices to cost:
- \( x = 4 \) (slices)
- \( y = 6 \) (dollars)
### Finding the Unit Rate
To understand the cost per slice, we can calculate the unit rate:
\[
\text{Cost per slice} = \frac{y}{x} = \frac{6}{4} = 1.5
\]
This means each slice of pizza costs $1.50.
### Equation of the Line
In the context of the linear relationship, the equation can be expressed as:
\[
y = mx
\]
where \( m \) is the slope (cost per slice).
Substituting the value we found:
\[
y = 1.5x
\]
### Graphing the Line
To graph this line, we need to plot points based on the equation \( y = 1.5x \).
#### Example Points
1. If \( x = 0 \), then \( y = 1.5(0) = 0 \) → Point (0, 0)
2. If \( x = 2 \), then \( y = 1.5(2) = 3 \) → Point (2, 3)
3. If \( x = 4 \), then \( y = 1.5(4) = 6 \) → Point (4, 6)
4. If \( x = 6 \), then \( y = 1.5(6) = 9 \) → Point (6, 9)
Now you can plot these points on a Cartesian coordinate system.
### Plotting the Graph
- On the x-axis, you would place the number of slices.
- On the y-axis, you would place the total cost in dollars.
- Use the points (0, 0), (2, 3), (4, 6), and (6, 9) to draw the line.
### Final Result
The line will be straight, starting at the origin (0, 0) and rising with a slope of 1.5. This line represents the proportional relationship between the number of pizza slices purchased and the total cost. Each point on the line corresponds to the cost of \( x \) slices of pizza, with the relationship defined by the equation \( y = 1.5x \).