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.

Question

Ray

Ray

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Answer 1

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!