Question 103·Easy·Linear Equations in Two Variables
The equation models the depth, in centimeters, of water in a bucket seconds after a faucet is turned on. What is the depth of the water 10 seconds after the faucet is turned on?
For linear modeling questions like this, first identify what each variable represents, then plug the given value directly into the equation and simplify step by step. Pay attention to the order of operations (multiply before adding), and always check that your final value makes sense with the context (here, a reasonable positive depth in centimeters).
Hints
Identify what is being asked
You are given an equation for depth in terms of time . Which value of does the question ask you to use?
Use substitution
Once you know the correct value of , replace in the equation with that number and write out the new expression for .
Evaluate carefully
Multiply before you add. First calculate times the number of seconds, then add .
Desmos Guide
Evaluate the expression for 10 seconds
In a Desmos expression line, type 4*10+2 and press Enter. The output Desmos shows is the depth of the water (in centimeters) after 10 seconds; compare that value to the answer choices.
Step-by-step Explanation
Interpret the equation and the variables
The equation is .
- represents the depth of the water (in centimeters).
- represents the time in seconds after the faucet is turned on. The number is the rate the depth increases (4 cm each second), and is the initial depth when .
Substitute the given time into the equation
We are asked for the depth 10 seconds after the faucet is turned on. That means .
Substitute into the equation :
Compute the depth and match it to the answer choices
Now calculate the right-hand side:
So the depth of the water after 10 seconds is centimeters, which corresponds to choice C) 42.