Equations for Functions

Multiple Select

Here is an equation that represents a function: $$72x+12y=60$$ . Select **all** the different equations that describe the same function:

• $$x=\frac{5}{6} - \frac{y}{6}$$

• $$y = 5 + 6x$$

• 
  $$2y + 12x = 10$$

• 
  $$y = 5 - 6x$$

• 
  $$120y + 720x = 600$$

Multiple Choice

What is the output for an input of 4 using the rule: Multiply by 4, then add 2?

• 14
• 22
• 10
• 18

Multiple Choice

Here is an input-output rule for a function: Multiply by 4, then add 2. Write an equation to represent the function.

• f(x) = x + 2
• f(x) = 4x + 2
• f(x) = 4x - 2
• f(x) = 2x + 4

Multiple Choice

Here is an input-output rule for a function: Multiply by 4, then add 2. What letter did you use for the independent variable? The dependent variable?

• m for independent variable, n for dependent variable
• x for independent variable, y for dependent variable
• a for independent variable, b for dependent variable
• p for independent variable, q for dependent variable

Multiple Choice

A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limit, until it reaches its destination 200 miles away. Let $$x$$ represent the amount of time in hours that the car is going 55 miles per hour, and let $$y$$ be the time in hours that the car is going 35 miles per hour. An equation describing the relationship is $$55x + 35y = 200.$$ If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?

• 2 hours

• 2.5 hours

• 3 hours

• 3.5 hours

Multiple Choice

A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limit, until it reaches its destination 200 miles away. Let $$x$$ represent the amount of time in hours that the car is going 55 miles per hour, and let $$y$$ be the time in hours that the car is going 35 miles per hour. An equation describing the relationship is $$55x + 35y = 200.$$ If the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour?

• 1.5 hours
• 1 hour
• 2 hours
• 4 hours

Open Ended

A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limit, until it reaches its destination 200 miles away. Let $$x$$ represent the amount of time in hours that the car is going 55 miles per hour, and let $$y$$ be the time in hours that the car is going 35 miles per hour. An equation describing the relationship is $$55x + 35y = 200.$$ If the car spends no time going 35 miles per hour, how long would the trip take? Explain your reasoning.

Multiple Choice

Together, the areas of the rectangles sum to 30 square centimeters. Which equation shows the relationship between $$x$$ and $$y$$ ?

• 4x + y = 30
• 3x + 2y = 30
• x + 5y = 30
• 2x + 3y = 30

Multiple Choice

Together, the areas of the rectangles sum to 30 square centimeters. What is the value of x if y is 6 cm?

• 6
• 10
• 8
• 4

Multiple Choice

A room's ceiling is 15 feet tall. An architect wants to include a window in the room that is 6 feet tall. The distance between the floor and the bottom of the window is $$b$$ feet. The distance between the ceiling and the top of the window is $$a$$ feet. This relationship can be described by the equation $$a = 15 - (b + 6)$$ . Which variable is independent based on the equation given?

• a

• b