GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A nutritionist is tracking a patient's weight loss. The patient's weight, W (in pounds), over d days is represented by the function W(d) = -0.5d + 200. What is the meaning of the y-intercept in this context?
- AIt takes 200 days for the patient to lose all weight.
- BThe patient loses 0.5 pounds per day.
- CThe patient's initial weight was 200 pounds.
- DThe patient will reach a minimum weight of 200 pounds.
Show answer & explanationAnswer & explanation
Correct answer: C. The patient's initial weight was 200 pounds.
In a linear function W(d) = md + b, 'b' represents the y-intercept. The y-intercept is the value of W when d=0. In this context, d=0 means 'at the start' or 'initial'. So, the y-intercept of 200 means the patient's initial weight was 200 pounds.
Why the other options are wrong
- A. This would mean W(200) = 0, which is -0.5(200) + 200 = -100 + 200 = 100, not 0.
- B. This describes the slope (-0.5), not the y-intercept.
- D. This is incorrect. The weight will continue to decrease linearly as days pass.
Interpreting Y-intercept
The y-intercept of a graph is the point where the graph crosses the y-axis. In a function, it represents the output value when the input value is zero, often signifying an initial amount, starting point, or fixed cost.
- In y = mx + b, 'b' is the y-intercept.
- To find it, set x=0 and solve for y.
- Its meaning is highly dependent on the context of the problem.
Memory trick: Y-intercept is the 'Y' at the 'start' (x=0)!