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# 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**

{% file src="/files/-LraxOD4BRIwQ6hd4ZOB" %}
Data Set 1
{% endfile %}

{% file src="/files/-LraxRXnSeHPcKZBVVEa" %}
Data Set 12
{% endfile %}

{% file src="/files/-LraxTVLnrMDK2r5rc9h" %}
Data Set 13
{% endfile %}

**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.