Question 1

Which of the following equations represents a linear function?

Accepted Answer

$$y = 2x + 5$$

Question 2

Given the equation $$3(x-4) = 2x - 1$$, what is the value of $$x$$?

Accepted Answer

$$x = 11$$

Question 3

Suppose the cost to run an electric air conditioning system is modeled by $$E(t) = 500t + 2000$$ and the cost to run a gas system is $$G(t) = 300t + 4000. $$After how many years will the total costs be equal?

Accepted Answer

$$t = 10$$

Question 4

Which of the following is NOT a characteristic of a linear equation?

Accepted Answer

The graph is a parabola.

Question 5

Solve for $$x in $$the equation $$\dfrac{x-2}{4} - \dfrac{1}{3}x = 5 - \dfrac{1}{12}(3-x).$$

Accepted Answer

$$x = 12$$

Question 6

A college’s tuition and fees during year $$t$$ are modeled by $$f(t) = 755.7(t-1985) + 6121. In $$what year will tuition reach $$30,000$$?

Accepted Answer

$$t = 2021$$

Question 7

If the cost to run an electric system is $$E(t) = 400t + 2500$$ and a gas system is $$G(t) = 600t + 1500$$, what is the cost when the two systems are equal?

Accepted Answer

$$4500$$

Question 8

Which of the following scenarios can be modeled by a linear function?

Accepted Answer

A car depreciates by $$2000$$ each year.

Question 9

Given the function $$f(t) = 755.7(t-1985) + 6121$$, what does the number $$755.7$$ represent in the context of tuition and fees?

Accepted Answer

The annual increase in tuition and fees.

Question 10

If the cost of electricity is modeled by $$E(t) = 450t + 1800$$ and the cost of gas is $$G(t) = 300t + 2700$$, after how many years will the cost of electricity be less than the cost of gas?

Accepted Answer

$$t \u003e 6$$

Question 11

Which of the following best describes the solution to a system of two linear equations when their graphs intersect at a single point?

Accepted Answer

There is one unique solution.

Question 12

A company’s profit $$P$$ after $$t$$ years is modeled by $$P(t) = 1200t - 5000. $$What does the $$-5000$$ represent?

Accepted Answer

The initial loss or investment.

Question 13

If $$y = mx + b is $$the equation of a line, what does $$m$$ represent?

Accepted Answer

The slope of the line.

Question 14

Which of the following equations is NOT linear?

Accepted Answer

$$y = 2x^2$ + 3$$

Question 15

A water tank is being filled at a constant rate. If the amount of water in the tank after $$t$$ hours is given by $$W(t) = 150t + 500$$, how much water was in the tank initially?

Accepted Answer

$$500$$ liters

Step-by-Step Guidance for Linear Functions and Equations (Air Conditioning Cost Example)

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