Praxis Math Quiz: Identify Linear Relationships
20 questions · exam conditions
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Identify Linear RelationshipsQuestion 1 of 20

A researcher collects data on the age of a car in years (x) and its resale value (y). The data points are (1, $20000), (3, $16000), (5, $12000), (7, $8000). What is the rate of change per year that defines this linear relationship?

The value decreases by $4,000 for every year the car ages.
The value decreases by $2,000 for every year the car ages.
The value increases by $2,000 for every year the car ages.
The value decreases by $1,000 for every year the car ages.
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Praxis Math Quiz

Praxis Math Quiz: Identify Linear Relationships

Practice Identify Linear Relationships in Praxis Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Identify Linear Relationships, giving you a quick way to practice the rules, question types, and explanations that matter most for Praxis Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A researcher collects data on the age of a car in years (x) and its resale value (y). The data points are (1, $20000), (3, $16000), (5, $12000), (7, $8000). What is the rate of change per year that defines this linear relationship?

  1. The value decreases by $4,000 for every year the car ages.
  2. The value decreases by $2,000 for every year the car ages. (correct answer)
  3. The value increases by $2,000 for every year the car ages.
  4. The value decreases by $1,000 for every year the car ages.
Explanation: To find the rate of change (slope), we can use any two points. Using (1, 20000) and (3, 16000), the change in y is $16000 - 20000=−20000 = -4000. The change in x is 3 - 1 = 2 years. The rate of change is -4000/2years=−4000 / 2 years = -2000 per year.

Question 2

A scientist observes that for every 10 meters a diver descends into the ocean, the ambient pressure increases by approximately 1 atmosphere. Which of the following best describes the relationship between a diver's depth and the ambient pressure?

  1. A strong positive linear relationship, where pressure increases with depth. (correct answer)
  2. A strong negative linear relationship, where pressure decreases with depth.
  3. A non-linear relationship, as the rate of pressure change varies.
  4. No discernible relationship between the depth and the ambient pressure.
Explanation: The pressure increases by a constant amount (1 atmosphere) for each constant interval of depth increase (10 meters). This constant rate of change is the definition of a linear relationship. Since pressure increases as depth increases, the relationship is positive and strong.

Question 3

A researcher is analyzing a set of data points representing a student's test scores over several weeks. The ordered pairs are (Week 1, 75), (Week 2, 78), (Week 3, 82), (Week 4, 85), and (Week 5, 89). Which statement best characterizes the relationship between the week number and the test score?

  1. A perfect negative linear relationship, with scores decreasing by 3 each week.
  2. A non-linear relationship because the increase in score is not identical each week.
  3. An approximately positive linear relationship, with scores generally increasing over time. (correct answer)
  4. No relationship, as the scores fluctuate without a clear pattern.
Explanation: The scores are consistently increasing. From week to week, the increases are +3, +4, +3, and +4. While not perfectly constant, the rate of change is very similar from week to week, suggesting a strong or approximately positive linear relationship. Real-world data often exhibits such minor variations.

Question 4

A real estate agent notices that for a particular neighborhood, the selling price of a house tends to increase as its square footage increases. If the data points representing this relationship on a scatterplot are widely spread out around a general upward trend, which term best describes the relationship?

  1. A strong positive linear relationship.
  2. A weak positive linear relationship. (correct answer)
  3. A strong negative linear relationship.
  4. A perfect non-linear relationship.
Explanation: The trend is upward ('price...tends to increase as...square footage increases'), so the relationship is positive. Because the points are 'widely spread out,' the relationship is weak. A strong relationship would have points clustered tightly around a line.

Question 5

A store manager observes that on days with higher temperatures, the store sells more bottles of water. If the data points for daily temperature and water bottles sold are plotted, they form a cluster that suggests a line of best fit could be drawn. What does this indicate?

  1. High temperatures cause an increase in water sales, confirming a perfect relationship.
  2. There is likely a positive linear association between temperature and water sales. (correct answer)
  3. There is likely a negative linear association between temperature and water sales.
  4. No valid conclusion can be drawn without a mathematical equation.
Explanation: The observation that 'more' water is sold on 'higher' temperature days indicates a positive association. Since the points form a cluster that a line could model, it suggests a linear relationship. However, correlation does not imply causation, and real-world data is rarely perfect, making 'positive linear association' the best description.

Question 6

A study measures the height of a plant each week. In week 1, it is 2 cm. In week 2, it is 4 cm. In week 3, it is 8 cm. In week 4, it is 16 cm. Which statement best describes the relationship between the number of weeks and the plant's height?

  1. There is a positive linear relationship, with the height increasing by 2 cm each week.
  2. There is a negative linear relationship, as the rate of growth is not constant.
  3. There is a non-linear relationship, as the height doubles each week. (correct answer)
  4. There is no relationship between the time passed and the height of the plant.
Explanation: The height increases by 2 cm, then 4 cm, then 8 cm. The amount of increase is not constant, so the relationship is not linear. Since the height is multiplied by a constant factor (2) each week, this is an exponential relationship, which is a type of non-linear relationship.

Question 7

A researcher states that for every two years of experience a person has, their salary tends to increase by $5,000. Another researcher studying a different field finds that for every one year of experience, salary tends to increase by $2,000. Which statement is the most accurate comparison of these two linear relationships?

  1. The first relationship has a steeper rate of change than the second. (correct answer)
  2. The second relationship has a steeper rate of change than the first.
  3. Both relationships show the same rate of salary increase per year of experience.
  4. It is impossible to compare the rates of change without the actual data points.
Explanation: To compare the rates of change (slopes), we should find the salary increase per year. In the first relationship, the rate is $5,000 / 2 years = $2,500 per year. In the second relationship, the rate is $2,000 / 1 year = $2,000 per year. Since $2,500 is greater than $2,000, the first relationship has a steeper rate of change.

Question 8

Data on the number of hours spent exercising per week (x) and resting heart rate in beats per minute (y) is collected. The data points are: (1, 80), (3, 72), (5, 64), (7, 56). Which of the following equations could model this linear relationship?

  1. y=4x+84y = 4x + 84
  2. y=−4x+84y = -4x + 84 (correct answer)
  3. y=−8x+88y = -8x + 88
  4. y=8x+72y = 8x + 72
Explanation: First, find the slope (rate of change). Using the first two points: m=(72−80)/(3−1)=−8/2=−4m = (72 - 80) / (3 - 1) = -8 / 2 = -4. This means the heart rate decreases by 4 bpm for each additional hour of exercise. Now, use the point-slope form with the point (1, 80): y−80=−4(x−1)y - 80 = -4(x - 1), which simplifies to y−80=−4x+4y - 80 = -4x + 4, or y=−4x+84y = -4x + 84. This equation correctly models the data.

Question 9

A scatterplot of data is described as follows: the points form a pattern that looks like a downward-sloping curve, not a straight line. Which of the following is the most appropriate description of the relationship?

  1. A positive linear relationship
  2. A negative linear relationship
  3. A negative non-linear relationship (correct answer)
  4. No relationship
Explanation: The pattern is 'downward-sloping', which indicates a negative relationship (as x increases, y decreases). The pattern is a 'curve, not a straight line,' which indicates it is non-linear. Therefore, it is a negative non-linear relationship.

Question 10

A data set shows a strong negative linear correlation between the number of winter coats sold and the average daily temperature. Which of the following is the most likely value for the correlation coefficient, rr?

  1. r=0.91r = 0.91
  2. r=0.12r = 0.12
  3. r=−0.09r = -0.09
  4. r=−0.88r = -0.88 (correct answer)
Explanation: A 'strong' correlation means the value of rr is close to -1 or +1. A 'negative' correlation means the value of rr must be negative. Of the choices, r=−0.88r = -0.88 is the only one that represents a strong negative linear relationship. r=0.91r = 0.91 is strong but positive. The other two values are very close to 0 and represent weak relationships.

Question 11

A car depreciates in value over time. A study of a particular car model shows its value (y) after a certain number of years (x). The data collected are: (1, $25,000), (2, $22,500), (3, $20,000), (4, $17,500). However, the researcher made a typo and recorded the fifth data point as (5, $16,000) instead of the actual value of $15,000. How does this single incorrect point affect the description of the linear relationship?

  1. It makes the negative linear relationship appear weaker than it actually is. (correct answer)
  2. It changes the relationship from a negative linear one to a positive one.
  3. It has no effect because the overall trend is still clearly negative.
  4. It makes the negative linear relationship appear stronger than it actually is.
Explanation: The actual data shows a perfect linear relationship where the value decreases by exactly $2,500 each year. The incorrect point (5, $16,000) deviates from this pattern (a decrease of only $1,500). This point is an outlier that does not fit the line, thus making the overall linear relationship appear less consistent and therefore weaker.

Question 12

A teacher plots the number of hours a student reports studying (x-variable) against their final exam score (y-variable). The data points generally show that students who study more get higher scores. However, one point, (2, 98), is far from the general trend of the other data. Most students who studied for 2 hours scored around 70. How should this data point be interpreted?

  1. As an outlier that weakens an otherwise positive linear relationship. (correct answer)
  2. As evidence that the relationship is actually a negative linear relationship.
  3. As the most important point for determining the y-intercept of the line.
  4. As proof that there is no relationship between hours studied and exam score.
Explanation: The point (2, 98) deviates significantly from the general positive trend. Such a point is called an outlier. Outliers tend to weaken the strength of a correlation and can pull the line of best fit away from the other data points.

Question 13

A researcher finds a linear relationship between the amount of fertilizer used on a field and the crop yield. For every 5 pounds of fertilizer added, the yield increases by 10 bushels. If using 10 pounds of fertilizer results in a yield of 40 bushels, what would be the expected yield if 0 pounds of fertilizer were used?

  1. 0 bushels
  2. 10 bushels
  3. 20 bushels (correct answer)
  4. 30 bushels
Explanation: The rate of change is 10 bushels per 5 pounds, which is 2 bushels per pound. This is the slope of the linear relationship. We have a point (10 pounds, 40 bushels). We want to find the yield at 0 pounds (the y-intercept). We can work backward: since going from 0 to 10 pounds means an increase of 10 pounds, the yield should increase by 10 * 2 = 20 bushels. So, the yield at 0 pounds must be 40 - 20 = 20 bushels.

Question 14

A researcher is studying the link between hours of television watched per day (x) and GPA (y) for a group of middle school students. The data suggests a moderate negative linear association. Which of the following conclusions is the most reasonable interpretation of this finding?

  1. Watching television causes a student's GPA to decrease, and the effect is very strong.
  2. Students who tend to watch more television also tend to have lower GPAs. (correct answer)
  3. Students who watch less television are guaranteed to have higher GPAs.
  4. There is no connection between television habits and academic performance.
Explanation: A moderate negative linear association means there is a trend where one variable tends to decrease as the other increases, but it is not a perfect relationship and does not prove causation. Option B correctly describes this association without claiming causation or certainty. Option A claims causation. Option C makes a guarantee, which is too strong for a moderate association. Option D contradicts the finding.

Question 15

The path of a ball thrown into the air is observed. The relationship between the time since the ball was thrown (x) and its height (y) is recorded. The data shows the height increasing for a period and then decreasing. This relationship is best described as:

  1. Linear, because the ball travels at a constant speed.
  2. Non-linear, because the height does not change at a constant rate. (correct answer)
  3. Negative linear, because the ball eventually comes down.
  4. Positive linear, because the ball initially goes up.
Explanation: The height increases and then decreases, which means the rate of change is not constant. A linear relationship must have a constant rate of change (either always increasing, always decreasing, or always constant). The described path is a parabola, which is a type of non-linear (specifically, quadratic) relationship.

Question 16

A taxi service charges a flat fee of $3.00 plus $2.00 for each mile traveled. If xx is the number of miles traveled and yy is the total cost of the ride, which statement accurately describes the relationship between xx and yy?

  1. A proportional relationship where the cost is always double the miles.
  2. A perfect positive linear relationship with a constant rate of change. (correct answer)
  3. A non-linear relationship because of the initial flat fee.
  4. A weak positive linear relationship since fares can vary.
Explanation: The relationship can be modeled by the equation y=2x+3y = 2x + 3. This is the equation of a line with a positive slope (2) and a y-intercept (3). For any number of miles, the cost will fall exactly on this line, so the relationship is a perfect positive linear one. It is not proportional because of the flat fee (a proportional relationship would pass through the origin).

Question 17

If a line of best fit for a scatterplot has the equation y=−3x+10y = -3x + 10, but most of the data points are very far from this line, how would the linear relationship be described?

  1. A strong positive linear relationship.
  2. A strong negative linear relationship.
  3. A weak negative linear relationship. (correct answer)
  4. A perfect negative linear relationship.
Explanation: The equation y=−3x+10y = -3x + 10 has a negative slope (-3), so the relationship is negative. However, the fact that 'most of the data points are very far from this line' indicates that the linear model is not a good fit for the data. This describes a weak relationship. A strong or perfect relationship would have points very close to the line.

Question 18

If two variables have a strong positive linear correlation, which of the following statements must be true?

  1. An increase in one variable causes an increase in the other variable.
  2. When one variable has a high value, the other variable is also likely to have a high value. (correct answer)
  3. The relationship between the variables can be perfectly described by the equation y = x.
  4. For every unit increase in one variable, the other variable increases by exactly one unit.
Explanation: A strong positive linear correlation indicates that high values of one variable are associated with high values of the other. It does not prove causation (A is wrong). The relationship does not have to be perfect or have a slope of 1 (C and D are wrong), it just needs to show a strong upward trend.

Question 19

A study finds a correlation coefficient of r=0.85r = 0.85 between daily ice cream sales and the number of people at a public pool. Which statement is the most valid interpretation?

  1. Eating ice cream causes more people to go to the pool to cool down.
  2. There is a strong positive linear relationship between ice cream sales and pool attendance. (correct answer)
  3. There is a weak negative linear relationship between ice cream sales and pool attendance.
  4. The relationship is positive but too weak to be considered significant.
Explanation: A correlation coefficient of 0.85 is close to +1, which indicates a strong positive linear relationship. This means that as one variable increases, the other tends to increase as well. It does not establish causation; a third variable, such as high temperature, is likely causing both to increase.

Question 20

A dataset contains five points. Four of the points lie perfectly on the line y=2x+3y = 2x + 3. One point, an outlier, is located at (5, 5). How does this outlier affect the perceived relationship?

  1. It strengthens the positive linear correlation by adding a new data point.
  2. It weakens the otherwise perfect positive linear correlation. (correct answer)
  3. It changes the relationship from positive to negative correlation.
  4. It has no effect on the correlation because it is only one point out of five.
Explanation: The point (5, 5) does not fit the pattern. According to the line y=2x+3y = 2x + 3, when x=5x=5, yy should be 2(5)+3=132(5) + 3 = 13. The point (5, 5) is far from this expected value. An outlier that does not fit the pattern of the other data points will always weaken the correlation, making the relationship appear less linear than it is.