Digital SATMath: AlgebraEasy
A botanist is studying the growth of a particular vine. The length of the vine, L, in centimeters, can be modeled by the equation L = 3t + 15, where t is the number of days after planting. What is the meaning of the number 15 in this equation?
- AThe maximum length the vine will reach.
- BThe rate at which the vine grows per day.
- CThe number of days it takes for the vine to grow 3 cm.
- DThe initial length of the vine when planted.
Show answer & explanationAnswer & explanation
Correct answer: D. The initial length of the vine when planted.
In a linear equation of the form y = mx + b, the 'b' term represents the y-intercept, which is the initial value of the dependent variable when the independent variable is zero. In this context, when t=0 (at planting), L=15.
Why the other options are wrong
- A. A linear equation suggests continuous growth, not a maximum length.
- B. This describes the coefficient of 't', which is the slope.
- C. This is a misinterpretation of the growth rate and initial value.
Y-intercept in Linear Equations
The y-intercept (b) in a linear equation y = mx + b represents the value of y when x is 0.
- It's the point where the line crosses the y-axis.
- Often represents an initial amount or starting value.
- In real-world scenarios, it's the value of the dependent variable when the independent variable is absent or at its starting point.
Memory trick: Slope is how it SLIDES, intercept is where it STARTS.