Literal Equations and Linear Equations

(Calculator allowed)

For the linear function f, the table gives some values of x and their corresponding values of f(x), where c is a constant. Which of the following equations defines f ?

• f(x) = x + c

• f(x) = x + 3c

• f(x) = cx + c

• f(x) = 3cx + 3c

(Calculator allowed)

The graph of a line in the xy-plane has a positive slope and intersects the y-axis at a point that has a negative y-coordinate. Which of the following could be an equation of the line?

• –3x + 2y = –5

• –3x + 2y = 5

• 3x + 2y = –5

• 3x + 2y = 5

(Calculator allowed)

The graph of the equation ax + ky = 6 is a line in the xy-plane, where a and k are constants. If the line contains the points

(–2,–6) and (0,–3), what is the value of k?

• –2

• –1

• 2

• 3

(Calculator allowed)

A researcher surveyed 200 adults selected at random from the city of Aldley and 300 adults selected at random from the suburb of Aldley. Each person surveyed was asked whether he or she owns a car. Some of the results are shown in the partially completed table.

The researcher found that an adult surveyed in the suburb of Aldley is twice as likely to own a car as an adult surveyed in the city of Aldley. Of the following, which would be the value of x?

• 120

• 160

• 210

• 240

(No calculator allowed)

In the system of equations, a and c are constants.

If the system of equations has an infinite number of solutions (x, y), what is the value of a?

• –1/2

• 0

• 1/2

• 3/2

(No Calculator allowed)

Blood volume, V_B, in a human can be determined using the equation V_B = V_P / (1 – H), where V_P is the plasma volume and H is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and plasma volume?

• H = 1 – (V_P / V_B)

• H = V_B / V_P

• H = 1 + (V_B / V_P)

• H = V_B – V_P

(No Calculator allowed)

ax = 5

In the equation above, a is a constant. For which of the following values of a will the equation have no solutions?

• 0

• 1

• 5

• 10

(No Calculator allowed)

If 3(3x + 5) = 2x – 8, what is the value of x?

• –23 ÷ 7

• –15 ÷ 7

• –13 ÷ 7

• 7 ÷ 11

For the linear function, h, the table shows several values of x and their corresponding values of h(x). Which of the following defines h?

• h(x) = 2x – 3

• h(x) = 3x – 5

• h(x) = 4x – 7

• h(x) = 4x – 9

(No Calculator allowed)

Terrence's car contains 8 gallons of fuel. He plans to drive the car m miles using the fuel currently in the car. If the car can drive 20 miles per gallon, which inequality gives the possible values of m?

• m ≤ (8)(20)

• m ≥ (8)(20)

• 8 ≤ 20m

• 8 ≥ 20m