GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A client is tracking their savings account balance. The balance (B) in dollars over time (t) in months is represented by the equation B = 150t + 500. What does the number 500 represent in this context?
- AThe amount added to the account each month
- BThe total amount saved after 150 months
- CThe initial amount deposited
- DThe monthly interest rate
Show answer & explanationAnswer & explanation
Correct answer: C. The initial amount deposited
In a linear equation y = mx + b, the 'b' term represents the y-intercept, which is the starting value or initial amount when x=0. Here, B is the balance and t is time, so 500 is the balance when t=0.
Why the other options are wrong
- A. The amount added each month is represented by the coefficient of t, which is 150.
- B. The total amount after 150 months would be 150(150) + 500, not just 500.
- D. The monthly interest rate would typically be a multiplier or part of an exponential function, not a constant added term.
Interpreting Y-intercept
The y-intercept of a linear equation (y = mx + b) represents the initial value or starting point of the dependent variable when the independent variable is zero.
- It's the point where the line crosses the y-axis.
- In real-world scenarios, it often signifies a starting amount, initial cost, or baseline value.
- It occurs when the independent variable (x) is 0.
Memory trick: The 'Y' in Y-intercept stands for 'Your Starting Point'!