A team is selling discount cards as a fundraiser. The table shows the number of cards sold and the remaining amount of money needed.
Discount Cards Fundraiser
| Cards Sold | Remainder of Goal |
| ---------- | ----------------- |
| 10 | $875 |
| 20 | $795 |
| 30 | $715 |
| 40 | $635 |
| 50 | $555 |
Which word describes the slope of the line representing the data in the table?
A. zero
B. undefined
C. negative
D. positive
Answer (2)
Calculate the slope using two points from the table: (10, 875) and (20, 795).
Apply the slope formula: m = x 2 − x 1 y 2 − y 1 .
Substitute the values: m = 20 − 10 795 − 875 = − 8 .
The slope is negative: n e g a t i v e .
Explanation
Understanding the Problem We are given a table showing the number of discount cards sold and the remaining amount of money needed. We need to determine whether the slope of the line representing the data in the table is zero, undefined, negative, or positive.
Calculating the Slope To determine the slope, we can use any two points from the table. Let's use the points (10, 875) and (20, 795). The slope, m , is given by the formula: m = x 2 − x 1 y 2 − y 1
Substituting the Values Plugging in the values, we get: m = 20 − 10 795 − 875 = 10 − 80 = − 8
Determining the Sign of the Slope Since the slope m = − 8 , it is a negative value. Therefore, the slope of the line representing the data in the table is negative.
Examples
Understanding the slope of a line can help businesses predict profits or losses. For example, if a company tracks its expenses and revenue over time, a negative slope might indicate that expenses are increasing faster than revenue, signaling a need for cost-cutting measures or increased sales efforts. Conversely, a positive slope would suggest that revenue is growing faster than expenses, indicating a healthy business trend. Analyzing slopes helps in making informed financial decisions.
The slope of the line representing the fundraiser data is calculated to be negative, indicating that as the number of cards sold increases, the remaining amount of money needed decreases. Therefore, the answer is C. negative.
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