Exploring Linear and Nonlinear Functions

Luis and Kate want to play two video games for a total of 45 minutes. They use variables x and y to represent the time spent on each game, Super Bologna Man and You Have to Cut the Wire, respectively. The relationship between these times is expressed as x + y = 45. The video explores whether this relationship can be represented as a linear equation, ultimately showing that it can be written in the form y = -x + 45, confirming it is linear.

What is the total amount of time Luis and Kate plan to spend playing both video games?

• 30 minutes

• 90 minutes

• 45 minutes

• 60 minutes

Which variable represents the time spent playing Super Bologna Man?

• x

• z

• y

• w

What does the variable y represent in the context of the video games?

• Time spent playing Super Bologna Man

• Time spent playing You Have to Cut the Wire

• Total time spent playing both games

• Number of games played

What equation represents the total time spent playing both games?

• x + y = 45

• x - y = 45

• x * y = 45

• x / y = 45

What is the first step to transform the equation x + y = 45 into the form y = mx + b?

• Subtract x from both sides

• Multiply both sides by x

• Divide both sides by x

• Add x to both sides

What is the slope (m) of the line in the equation y = -x + 45?

• -45

• 45

• -1

• 1

What is the y-intercept (b) in the equation y = -x + 45?

• 45

• -1

• 1

• -45

Which form is used to identify a linear relationship?

• y = mx - b

• y = m - bx

• y = m + bx

• y = mx + b

What does the equation y = -x + 45 tell us about the relationship between x and y?

• x and y are not related

• As x increases, y decreases

• As x decreases, y decreases

• As x increases, y increases

Can the relationship between the time spent on the two games be represented using a linear equation?

• Only if y is greater than x

• Only if x is greater than y

• Yes

• No