Question
The student store sells pencils for $0.75 each and erasers for $0.25 each. A student can buy a bundle that consists of 2 pencils and 1 eraser for a $0.50 discount. Graph the line that represents the cost a student would pay if he or she bought any number of bundles.
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Answers
GPT-4o mini
To graph the cost of bundles of pencils and erasers, we can start by determining the cost of a bundle.
### Price Calculation for a Bundle:
- **Cost of 2 pencils**: 2 pencils × $0.75/pencil = $1.50
- **Cost of 1 eraser**: 1 eraser × $0.25/eraser = $0.25
- **Total cost for 2 pencils and 1 eraser**: $1.50 (pencils) + $0.25 (eraser) = $1.75
- **Discount for the bundle**: $0.50
### Cost of the Bundle:
- **Cost of one bundle**: $1.75 (total cost) - $0.50 (discount) = $1.25
### Graphing the Cost:
Let \( x \) be the number of bundles purchased, and \( y \) be the total cost. The relationship can be represented by the equation:
\[
y = 1.25x
\]
### Steps to Graph:
1. Create a table of values:
- If \( x = 0 \) (no bundles), \( y = 1.25(0) = 0 \)
- If \( x = 1 \) (1 bundle), \( y = 1.25(1) = 1.25 \)
- If \( x = 2 \) (2 bundles), \( y = 1.25(2) = 2.50 \)
- If \( x = 3 \) (3 bundles), \( y = 1.25(3) = 3.75 \)
- If \( x = 4 \) (4 bundles), \( y = 1.25(4) = 5.00 \)
2. Plot these points on the graph:
- (0, 0)
- (1, 1.25)
- (2, 2.50)
- (3, 3.75)
- (4, 5.00)
3. Draw a straight line through the points. The line will start at the origin (0, 0) and slope upward, indicating that as the number of bundles increases, the cost also increases.
### Summary of the Graph:
- The graph represents a linear function where the slope is 1.25, indicating the cost increases by $1.25 for every additional bundle purchased. The line will intersect the y-axis at (0, 0), indicating there is no cost if no bundles are purchased.
Feel free to use graphing tools or software to plot these points accurately!
### Price Calculation for a Bundle:
- **Cost of 2 pencils**: 2 pencils × $0.75/pencil = $1.50
- **Cost of 1 eraser**: 1 eraser × $0.25/eraser = $0.25
- **Total cost for 2 pencils and 1 eraser**: $1.50 (pencils) + $0.25 (eraser) = $1.75
- **Discount for the bundle**: $0.50
### Cost of the Bundle:
- **Cost of one bundle**: $1.75 (total cost) - $0.50 (discount) = $1.25
### Graphing the Cost:
Let \( x \) be the number of bundles purchased, and \( y \) be the total cost. The relationship can be represented by the equation:
\[
y = 1.25x
\]
### Steps to Graph:
1. Create a table of values:
- If \( x = 0 \) (no bundles), \( y = 1.25(0) = 0 \)
- If \( x = 1 \) (1 bundle), \( y = 1.25(1) = 1.25 \)
- If \( x = 2 \) (2 bundles), \( y = 1.25(2) = 2.50 \)
- If \( x = 3 \) (3 bundles), \( y = 1.25(3) = 3.75 \)
- If \( x = 4 \) (4 bundles), \( y = 1.25(4) = 5.00 \)
2. Plot these points on the graph:
- (0, 0)
- (1, 1.25)
- (2, 2.50)
- (3, 3.75)
- (4, 5.00)
3. Draw a straight line through the points. The line will start at the origin (0, 0) and slope upward, indicating that as the number of bundles increases, the cost also increases.
### Summary of the Graph:
- The graph represents a linear function where the slope is 1.25, indicating the cost increases by $1.25 for every additional bundle purchased. The line will intersect the y-axis at (0, 0), indicating there is no cost if no bundles are purchased.
Feel free to use graphing tools or software to plot these points accurately!