Linear Functions: Graphing and Writing Equations for Nursing Students

Question 1

What is the slope-intercept form of a linear function with a slope of 3 and a y-intercept of -5?

Accepted Answer

y = 3x - 5

Answer

y = 5x - 3

Answer

y = -3x + 5

Question 2

The equation of a line that is perpendicular to the line y = 2x - 5 and passes through the point (3, 4) is:

Accepted Answer

y = -1/2x + 7

Answer

y = -2x + 11

Answer

y = 1/2x + 1

Answer

y = 2x - 2

Question 3

The equation of a line passing through the origin and parallel to the line y = 3x + 2 is:

Accepted Answer

y = 3x

Answer

y = 3x + 2

Answer

y = 2x

Answer

y = 2x + 2

Question 4

In a linear function, the y-intercept represents:

Accepted Answer

The value of y when x equals 0

Answer

The value of x when y equals 0

Answer

The slope of the line

Answer

The point where the line changes direction

Question 5

Identify the equation that represents a horizontal line.

Accepted Answer

y = 5

Answer

y = x - 1

Answer

y = 2x + 3

Answer

y = -3x + 2

Question 6

Express the equation of a line with a slope of 1/2 and a y-intercept of -1 in slope-intercept form.

Accepted Answer

y = 1/2x - 1

Answer

y = -1/2x - 1

Answer

y = 1/2x + 1

Answer

y = 2x - 1

Question 7

Select the graph that represents the linear function y = -x + 2:

Accepted Answer

(Image of a downward sloping line with an equation of y = -x + 2)

Answer

(Image of an upward sloping line with an equation of y = x + 2)

Answer

(Image of a circle)

Answer

(Image of a parabola)

Question 8

A practical example of a linear function application in nursing is:

Accepted Answer

Calculating drug dosage based on patient weight

Answer

Diagnosing diseases

Answer

Administering injections

Question 9

For the function y = 1/(x - 2), what is its domain?

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

x > 2

Question 10

To vertically translate the graph of y = x by 3 units, which transformation is applied?

Accepted Answer

y = x + 3

Answer

y = 3x

Answer

y = x - 3

Answer

y = 3 - x

Question 11

A nurse's daily patient count can be modeled by the linear function f(x) = 2x + 5, where x represents the number of hours worked. How many patients will the nurse see if she works 6 hours?

Accepted Answer

17

Answer

31

Answer

23

Answer

11

Question 12

Determine the domain of the linear function f(x) = (x - 2)/(x + 1).

Accepted Answer

All real numbers except -1

Answer

All positive real numbers

Answer

All real numbers

Answer

All negative real numbers

Question 13

Select the equation that describes a linear function with a slope of 0 and a y-intercept of 5.

Accepted Answer

y = 5

Answer

y = x + 5

Answer

y = 5x

Answer

y = 5x + 1

Question 14

What is the slope of the line represented by the equation 2x + 3y = 6?

Accepted Answer

-2/3

Answer

2/3

Answer

-3/2

Answer

3/2

Question 15

Calculate the slope of the line passing through the points (2, 5) and (4, 9).

Accepted Answer

2

Answer

-2

Answer

4

Answer

1

Question 16

Identify the domain of the function f(x) = 2x + 3.

Accepted Answer

Set of all real numbers

Answer

Set of negative real numbers

Answer

Set of positive real numbers

Answer

Set of integers

Question 17

Which of the following is NOT a defining characteristic of a linear function?

Accepted Answer

It is a non-linear function.

Answer

It can be represented as a straight line on a graph.

Answer

It can be defined by a linear equation.

Answer

It has a constant rate of change.

Question 18

Which of the following equations represents a linear function?

Accepted Answer

y = 3x + 2

Answer

y = e^x

Answer

y = x^2 + 2x + 1

Answer

y = sin(x)

Question 19

Which of the following is the equation of the line with a slope of -2 and a y-intercept of 1?

Accepted Answer

y = -2x + 1

Answer

y = -2x - 1

Answer

y = 2x + 1

Answer

y = 2x - 1

Question 20

Which of the following graphs represents a line with a negative slope?

Accepted Answer

Image of a line sloping downwards from left to right

Answer

Image of a vertical line

Answer

Image of a line sloping upwards from left to right

Answer

Image of a horizontal line

Question 21

For the linear function f(x) = 5x - 2, what is the x-intercept?

Accepted Answer

0.4

Answer

-5

Answer

2

Answer

10

Question 22

For the linear function f(x) = 3x + 2, what is the y-intercept?

Accepted Answer

2

Answer

0

Answer

-2

Answer

3

Question 23

What is the equation of the line perpendicular to y = 2x - 3 and passing through the point (2, 5)?

Accepted Answer

y = -1/2x + 6

Answer

y = -2x + 6

Answer

y = 2x + 6

Answer

y = 1/2x + 6

Question 24

Which of the following is a direct application of linear functions in nursing practice?

Accepted Answer

Calculating medication dosages based on patient weight and drug concentration.

Answer

Diagnosing illnesses based on a comprehensive medical history and physical examination.

Answer

Predicting disease outbreaks using complex epidemiological models.

Question 25

Which of the following equations represents a linear function?

Accepted Answer

y = 2x + 5

Answer

y = sin(x)

Answer

y = x^2 - 1

Answer

y = e^x

Question 26

A nurse needs to prepare a medication solution using a drug with a concentration of 100 mg per 500 ml of solution. How many mg of the drug are needed for 300 ml of solution?

Accepted Answer

60 mg

Answer

100 mg

Answer

200 mg

Answer

50 mg

Question 27

Which graph represents the linear equation y = -3x + 2?

Accepted Answer

(Graph of a line with a slope of -3 and a y-intercept of 2)

Answer

(Graph of a parabola)

Answer

(Graph of a circle)

Question 28

What is the equation of the line perpendicular to y = 2x + 1 and passing through the point (2, 5)?

Accepted Answer

y = -0.5x + 6

Answer

y = -2x + 1

Answer

y = 2x + 3

Answer

y = 0.5x + 4

Question 29

A patient's heart rate is recorded over time as (0 minutes, 80 bpm), (1 minute, 85 bpm), and (2 minutes, 90 bpm). What type of function best models this data?

Accepted Answer

Linear

Answer

Quadratic

Answer

Exponential

Answer

Trigonometric

Question 30

Which of the following is NOT a valid method for determining if two lines are parallel?

Accepted Answer

Comparing their y-intercepts.

Answer

Examining if their graphs are collinear.

Answer

Checking if their slopes are equal.

Answer

Determining if their equations have the same slope.

Question 31

Find the equation of the line passing through the point (2, 5) with a slope of -3.

Accepted Answer

y = -3x + 11

Answer

y = x - 5

Answer

y = 3x + 5

Answer

y = -x + 3

Question 32

Calculate the slope of the line perpendicular to the line 2x + 3y = 6.

Accepted Answer

1/3

Answer

-1/3

Answer

3

Question 33

Identify the graph of the linear function f(x) = 2x - 5 from the provided options.

Accepted Answer

[Image of a graph of a line with a slope of 2 and a y-intercept of -5]

Answer

[Image of a graph of a parabola opening upwards]

Answer

[Image of a graph of a line with a slope of -2 and a y-intercept of 5]

Question 34

Determine the slope of the line passing through the points (-2, 3) and (4, 7).

Accepted Answer

2/3

Answer

3/2

Answer

-2/3

Answer

-3/2

Question 35

Find the equation of the line perpendicular to the line 2x + y = 5 and passing through the point (2, 3).

Accepted Answer

y = -x + 7

Answer

y = 2x + 1

Answer

y = x + 1

Question 36

Which of the following accurately represents the domain of the linear function f(x) = 3x - 2?

Accepted Answer

All real numbers

Answer

x < 2

Answer

x ≠ 0

Answer

x > 2

Question 37

What is the range of the linear function f(x) = 2x + 1?

Accepted Answer

All real numbers

Answer

y > 1

Answer

y < 1

Answer

y ≠ 0

Question 38

A nurse is monitoring a patient's blood pressure. After 1 hour, the patient's systolic blood pressure is 120 mmHg, and after 3 hours, it is 110 mmHg. Assuming a linear relationship, what is the patient's expected systolic blood pressure after 5 hours?

Accepted Answer

100 mmHg

Answer

115 mmHg

Answer

95 mmHg

Answer

105 mmHg

Question 39

Which of the following equations represents a linear function?

Accepted Answer

y = 2x - 5

Answer

y = 2^x

Answer

y = x^2 + 3

Answer

y = 1/x

Question 40

What is the slope of the line represented by the equation y = -3x + 4?

Accepted Answer

-3

Answer

4

Answer

3

Question 41

A nurse is administering medication to a patient. The initial dose is 100 mg, and the dosage decreases by 5 mg every hour. What is the equation of the line representing the medication dosage over time?

Accepted Answer

y = -5x + 100

Answer

y = -100x + 5

Answer

y = 100x - 5

Answer

y = 5x + 100

Question 42

The graph of a linear function intersects the y-axis at the point (0, 2). What is the y-intercept of the function?

Accepted Answer

2

Answer

0

Answer

-2

Answer

1

Question 43

Which of the following pairs of points represents a line with a negative slope?

Accepted Answer

(1, 5) and (3, 1)

Answer

(2, 3) and (4, 6)

Answer

(0, 2) and (2, 4)

Question 44

A nurse is monitoring a patient's temperature. The patient's temperature is 98.6°F at 8:00 AM and 99.2°F at 10:00 AM. What is the rate of change of the patient's temperature in degrees Fahrenheit per hour?

Accepted Answer

0.3 degrees Fahrenheit per hour

Answer

0.6 degrees Fahrenheit per hour

Answer

1.2 degrees Fahrenheit per hour

Question 45

What is the equation of the line that passes through the points (2, 4) and (4, 8)?

Accepted Answer

y = 2x

Answer

y = -2x + 8

Answer

y = x + 2

Answer

y = x + 4

Question 46

A nurse is administering a medication intravenously. The IV bag contains 500 ml of solution, and the flow rate is 25 ml per hour. How long will it take for the IV bag to empty?

Accepted Answer

20 hours

Answer

15 hours

Answer

25 hours

Answer

10 hours

Question 47

Which of the following statements about linear functions is FALSE?

Accepted Answer

The graph of a linear function is always a curved line.

Answer

The y-intercept of a linear function is the point where the line crosses the y-axis.

Answer

The slope of a linear function represents the rate of change.

Question 48

A nurse is monitoring a patient's blood pressure. The initial reading is 120/80 mmHg, and it decreases by 5 mmHg every hour. Which linear equation represents the patient's systolic blood pressure (S) after *h* hours?

Accepted Answer

S = 120 - 5h

Answer

S = 80 + 5h

Answer

S = 80 - 5h

Answer

S = 120 + 5h

Question 49

What is the slope of the line passing through the points (2, 5) and (4, 11)?

Accepted Answer

3

Answer

-1/3

Answer

1/3

Answer

-3

Question 50

A patient's body temperature is increasing at a constant rate. The temperature was 98.6°F at 8:00 AM and 100.2°F at 10:00 AM. What is the rate of change in the patient's temperature per hour?

Accepted Answer

0.8°F per hour

Answer

0.4°F per hour

Answer

2.0°F per hour

Answer

1.6°F per hour

Question 51

Which of the following represents the equation of a line with a slope of -2 and a y-intercept of 3?

Accepted Answer

y = -2x + 3

Answer

y = 2x + 3

Answer

y = -2x - 3

Answer

y = 2x - 3

Question 52

A nurse is administering medication intravenously. The initial dosage is 100 mg, and the medication is being infused at a rate of 5 mg per minute. Which equation represents the total dosage (D) administered after *t* minutes?

Accepted Answer

D = 100 + 5t

Answer

D = 100 - 5t

Answer

D = 100t

Answer

D = 5t

Question 53

What is the y-intercept of the line represented by the equation 3x - 2y = 6?

Accepted Answer

-3

Answer

-2

Answer

3

Answer

2

Question 54

A patient's weight is decreasing at a steady rate.  If the patient weighed 180 pounds on Monday and 174 pounds on Friday, what is the average rate of weight loss per day?

Accepted Answer

1.2 pounds per day

Answer

2.4 pounds per day

Answer

1.5 pounds per day

Answer

0.6 pounds per day

Question 55

Which of the following equations represents a horizontal line?

Accepted Answer

y = 5

Answer

x = 5

Answer

y = 5x

Question 56

The graph of a linear function passes through the points (0, -2) and (4, 6). What is the equation of the line in slope-intercept form?

Accepted Answer

y = 2x - 2

Answer

y = 2x + 2

Answer

y = -2x - 2

Answer

y = -2x + 2

Question 57

A nurse is charting a patient's vital signs. The patient's pulse rate is 72 beats per minute and is decreasing at a rate of 2 beats per minute.  Which linear equation represents the patient's pulse rate (P) after *t* minutes?

Accepted Answer

P = 72 - 2t

Answer

P = 72t

Answer

P = 2t - 72

Answer

P = 72 + 2t