Math Problem Statement
For the equation y=−2x+100y=−2x+100, describe what the slope (-2) and y-intercept (100) might mean if this equation represents the balance in a savings account after spending a fixed amount each week.
Solution
In the equation , which could represent the balance in a savings account after spending a fixed amount each week, the slope and y-intercept have specific interpretations in this context.
Slope (-2)
The slope, , represents the rate of change in the balance of the savings account per week. Since it is negative, it indicates a decrease in the balance over time. Specifically, this slope tells us that every week, the balance decreases by 2 units. If we assume "units" to be dollars, this would mean that $2 is spent from the account each week.
In other words, for each additional week (as increases by 1), the balance decreases by 2 dollars.
Y-intercept (100)
The y-intercept, , represents the starting balance in the savings account when , which is the initial time or the beginning of the observation period. In this context, the y-intercept indicates that the account started with a balance of $100.
Interpretation Summary
If this equation models the balance in a savings account where a fixed amount is spent each week:
- The slope of implies a weekly expenditure of $2, leading to a steady decline in the balance.
- The y-intercept of indicates that the initial balance in the savings account was $100 at the beginning of this period.
Would you like more details or have any questions?
Related Questions:
- How would the equation change if $3 were spent each week instead?
- What would the slope be if the account balance increased by $5 each week instead of decreasing?
- How would the balance change after 10 weeks, according to this equation?
- What would the equation look like if the initial balance were $200 instead of $100?
- If the goal is to keep the account balance above zero, how many weeks would it take for the balance to reach zero?
Tip:
When analyzing linear equations in real-world contexts, the slope often represents a rate (like spending or earning per time period), and the y-intercept represents the initial amount or starting point.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope and Y-Intercept
Rate of Change
Formulas
y = mx + b
Theorems
Concept of Slope and Intercept in Linear Equations
Suitable Grade Level
Grades 8-10