10-1. Exercises

1. BASIC

Ex 1. A line has equation $y=0.5x+2$ .

1. Pick five distinct x-values, use the equation to compute the corresponding y-values, and plot the five points obtained.

2. Give the value of the slope of the line; give the value of the y-intercept.

Ex 2. A line has equation $y=x−0.5$ .

1. Pick five distinct x-values, use the equation to compute the corresponding y-values, and plot the five points obtained.

2. Give the value of the slope of the line; give the value of the y-intercept.

Ex 3. A line has equation $y=−2x+4$ .

1. Pick five distinct x-values, use the equation to compute the corresponding y-values, and plot the five points obtained.

2. Give the value of the slope of the line; give the value of the y-intercept.

Ex 4. A line has equation $y=−1.5x+1$ .

1. Pick five distinct x-values, use the equation to compute the corresponding y-values, and plot the five points obtained.

2. Give the value of the slope of the line; give the value of the y-intercept.

Ex 5. Based on the information given about a line, determine how y will change (increase, decrease, or stay the same) when x is increased, and explain. In some cases it might be impossible to tell from the information given.

1. The slope is positive.

2. The y-intercept is positive.

3. The slope is zero.

Ex 6. Based on the information given about a line, determine how $y$ will change (increase, decrease, or stay the same) when $x$ is increased, and explain. In some cases it might be impossible to tell from the information given.

1. The y-intercept is negative.

2. The y-intercept is zero.

3. The slope is negative.

Ex 7. A data set consists of eight $(x,y)$ pairs of numbers: (0, 12) (4, 16) ( 8, 22) (15, 28) (2, 15) (5, 14) (13, 24) (20, 30)

1. Plot the data in a scatter diagram.

2. Based on the plot, explain whether the relationship between $x$ and $y$ appears to be deterministic or to involve randomness.

3. Based on the plot, explain whether the relationship between $x$ and $y$ appears to be linear or not linear.

Ex 8. A data set consists of ten $(x,y)$ pairs of numbers: (3, 20) (6, 9) (11, 0) (14, 1) (18, 9) (5, 13) (8, 4) (12, 0) (17, 6) (20, 16)

1. Plot the data in a scatter diagram.

2. Based on the plot, explain whether the relationship between $x$ and $y$ appears to be deterministic or to involve randomness.

3. Based on the plot, explain whether the relationship between $x$ and $y$ appears to be linear or not linear.

Ex 9. A data set consists of nine $(x,y)$ pairs of numbers: (8, 16) (10, 4) (12, 0) (14, 4) (16, 16) (9, 9) (11, 1) (13, 1) (15, 9)

1. Plot the data in a scatter diagram.

2. Based on the plot, explain whether the relationship between $x$ and $y$ appears to be deterministic or to involve randomness.

3. Based on the plot, explain whether the relationship between $x$ and $y$ appears to be linear or not linear.

Ex 10. A data set consists of five $(x,y)$ pairs of numbers: (0, 1) (2, 5) (3, 7) (5, 11) (8, 17)

1. Plot the data in a scatter diagram.

2. Based on the plot, explain whether the relationship between $x$ and $y$ appears to be deterministic or to involve randomness.

3. Based on the plot, explain whether the relationship between $x$ and $y$ appears to be linear or not linear.

2. APPLICATIONS

Ex 11. At 60°F a particular blend of automotive gasoline weights 6.17 lb/gal. The weight y of gasoline on a tank truck that is loaded with $x$ gallons of gasoline is given by the linear equation $y=6.17x$.

1. Explain whether the relationship between the weight $y$ and the amount $x$ of gasoline is deterministic or contains an element of randomness.

2. Predict the weight of gasoline on a tank truck that has just been loaded with 6,750 gallons of gasoline.

Ex 12. The rate for renting a motor scooter for one day at a beach resort area is $25 plus 30 cents for each mile the scooter is driven. The total cost $y$ in dollars for renting a scooter and driving it x miles is $y=0.30x+25$

1. Explain whether the relationship between the cost $y$ of renting the scooter for a day and the distance $x$ that the scooter is driven that day is deterministic or contains an element of randomness.

2. A person intends to rent a scooter one day for a trip to an attraction 17 miles away. Assuming that the total distance the scooter is driven is 34 miles, predict the cost of the rental.

Ex 13. The pricing schedule for labor on a service call by an elevator repair company is $150 plus $50 per hour on site.

1. Write down the linear equation that relates the labor cost $y$ to the number of hours $x$ that the repairman is on site.

2. Calculate the labor cost for a service call that lasts 2.5 hours.

Ex 14. The cost of a telephone call made through a leased line service is 2.5 cents per minute.

1. Write down the linear equation that relates the cost $y$ (in cents) of a call to its length $x$ .

2. Calculate the cost of a call that lasts 23 minutes.

3. LARGE DATA SET EXERCISES

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data1.xls

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data12.xls

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data13.xls

Ex 15. Large Data Set 1 lists the SAT scores and GPAs of 1,000 students. Plot the scatter diagram with SAT score as the independent variable ($x$) and GPA as the dependent variable ($y$). Comment on the appearance and strength of any linear trend.

Ex 16. Large Data Set 12 lists the golf scores on one round of golf for 75 golfers first using their own original clubs, then using clubs of a new, experimental design (after two months of familiarization with the new clubs). Plot the scatter diagram with golf score using the original clubs as the independent variable ($x$) and golf score using the new clubs as the dependent variable ($y$). Comment on the appearance and strength of any linear trend.

Ex 17. Large Data Set 13 records the number of bidders and sales price of a particular type of antique grandfather clock at 60 auctions. Plot the scatter diagram with the number of bidders at the auction as the independent variable ($x$) and the sales price as the dependent variable ($y$). Comment on the appearance and strength of any linear trend.