Question 40·Easy·Linear Equations in Two Variables
A wildlife rehabilitation center is filling a small pond for turtles. At time , the pond contains liters of water. Water is added at a constant rate of liters per minute.
Which choice is the equation that gives the volume of water (in liters) in the pond after minutes?
When a quantity starts at an initial value and changes at a constant rate, model it with . The initial value (at ) is , and the “per 1 unit” rate is . Match those two numbers to the correct equation.
Hints
Find the value when
The amount at is the intercept in a linear equation.
Use the constant rate as the slope
“ liters per minute” tells you how much changes when increases by 1.
Put it into
Use from the rate and from the starting amount to form the equation.
Desmos Guide
Enter the situation as a linear form
In Desmos, note that the model should have the form .
Test each choice at
For each option, evaluate the value when . The correct equation must give .
Check the rate for a 1-minute increase
Compare the value at to the value at . The correct equation should increase by liters.
Step-by-step Explanation
Identify the starting value and the rate
The pond starts with liters when , so the intercept is . It increases by liters each minute, so the slope is .
Write the linear equation
Using with and , the equation is .