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4.5E: Exercises

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Practice Makes Perfect

Recognize the Relation Between the Graph and the Slope–Intercept Form of an Equation of a Line

In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation y=mx+b.

Exercise 4.5E.1

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 5) and (1, negative 2).

y=3x5

Exercise 4.5E.2

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1,2).

y=4x2

Answer

slope m=4 and y-intercept (0,2)

Exercise 4.5E.3

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,4) and (1,3).

y=x+4

Exercise 4.5E.4

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (1, negative 2).

y=3x+1

Answer

slope m=3 and y-intercept (0,1)

Exercise 4.5E.5

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 3).

y=43x+1

Exercise 4.5E.6

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,3) and (1,5).

y=25x+3

Answer

slope m=25 and y -intercept (0,3)

Identify the Slope and y-Intercept From an Equation of a Line

In the following exercises, identify the slope and y-intercept of each line.

Exercise 4.5E.7

y=7x+3

Exercise 4.5E.8

y=9x+7

Answer

m=9; y-intercept: (0,7)

Exercise 4.5E.9

y=6x8

Exercise 4.5E.10

y=4x10

Answer

m=4; y-intercept: (0,10)

Exercise 4.5E.11

3x+y=5

Exercise 4.5E.12

4x+y=8

Answer

m=4\0;\(y-intercept: (0,8)

Exercise 4.5E.13

6x+4y=12

Exercise 4.5E.14

8x+3y=12

Answer

m=83; y-intercept: (0,4)

Exercise 4.5E.15

5x2y=6

Exercise 4.5E.16

7x3y=9

Answer

m=73; y-intercept: (0,3)

Graph a Line Using Its Slope and Intercept

In the following exercises, graph the line of each equation using its slope and y-intercept.

Exercise 4.5E.17

y=x+3

Exercise 4.5E.18

y=x+4

Answer

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 4) and (1, 5).

Exercise 4.5E.19

y=3x1

Exercise 4.5E.20

y=2x3

Answer

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (1, negative 1).

Exercise 4.5E.21

y=x+2

Exercise 4.5E.22

y=x+3

Answer

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 3) and (1, 2).

Exercise 4.5E.23

y=x4

Exercise 4.5E.24

y=x2

Answer

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (1, negative 3).

Exercise 4.5E.25

y=34x1

Exercise 4.5E.26

y=25x3

Answer

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 3) and (5, negative 5).

Exercise 4.5E.27

y=35x+2

Exercise 4.5E.28

y=23x+1

Answer

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0,1) and (3, negative 1).

Exercise 4.5E.29

3x4y=8

Exercise 4.5E.30

4x3y=6

Answer

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, negative 2) and (3,2).

Exercise 4.5E.31

y=0.1x+15

Exercise 4.5E.32

y=0.3x+25

Answer

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The line goes through the points (0, 25) and (negative 50, 10).

Choose the Most Convenient Method to Graph a Line

In the following exercises, determine the most convenient method to graph each line.

Exercise 4.5E.33

x=2

Exercise 4.5E.34

y=4

Answer

horizontal line

Exercise 4.5E.35

y=5

Exercise 4.5E.36

x=3

Answer

vertical line

Exercise 4.5E.37

y=3x+4

Exercise 4.5E.38

y=5x+2

Answer

slope–intercept

Exercise 4.5E.39

xy=5

Exercise 4.5E.40

xy=1

Answer

intercepts

Exercise 4.5E.41

y=23x1

Exercise 4.5E.42

y=45x3

Answer

slope–intercept

Exercise 4.5E.43

y=3

Exercise 4.5E.44

y=1

Answer

horizontal line

Exercise 4.5E.45

3x2y=12

Exercise 4.5E.46

2x5y=10

Answer

intercepts

Exercise 4.5E.47

y=14x+3

Exercise 4.5E.48

y=13x+5

Answer

slope–intercept

Graph and Interpret Applications of Slope–Intercept

Exercise 4.5E.49

The equation P=31+1.75w models the relation between the amount of Tuyet’s monthly water bill payment, P, in dollars, and the number of units of water, w, used.

  1. Find Tuyet’s payment for a month when 0 units of water are used.
  2. Find Tuyet’s payment for a month when 12 units of water are used.
  3. Interpret the slope and P-intercept of the equation.
  4. Graph the equation.
Exercise 4.5E.50

The equation P=28+2.54w models the relation between the amount of Randy’s monthly water bill payment, P, in dollars, and the number of units of water, w, used.

  1. Find the payment for a month when Randy used 0 units of water.
  2. Find the payment for a month when Randy used 15 units of water.
  3. Interpret the slope and P-intercept of the equation.
  4. Graph the equation.
Answer
  1. $28
  2. $66.10
  3. The slope, 2.54, means that Randy’s payment, P, increases by $2.54 when the number of units of water he used, w, ncreases by 1. The P-intercept means that if the number units of water Randy used was 0, the payment would be $28.

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 2 to 20. The y-axis of the plane represents the variable P and runs from negative 1 to 100. The line begins at the point (0, 28) and goes through the point (15, 66.1).

Exercise 4.5E.51

Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day.

  1. Find the amount Bruce is reimbursed on a day when he drives 0 miles.
  2. Find the amount Bruce is reimbursed on a day when he drives 220 miles.
  3. Interpret the slope and R-intercept of the equation.
  4. Graph the equation.
Exercise 4.5E.52

Janelle is planning to rent a car while on vacation. The equation C=0.32m+15 models the relation between the cost in dollars, C, per day and the number of miles, m, she drives in one day.

  1. Find the cost if Janelle drives the car 0 miles one day.
  2. Find the cost on a day when Janelle drives the car 400 miles.
  3. Interpret the slope and C-intercept of the equation.
  4. Graph the equation.
Answer
  1. $15
  2. $143
  3. The slope, 0.32, means that the cost, C, increases by $0.32 when the number of miles driven, m, increases by 1. The C-intercept means that if Janelle drives 0 miles one day, the cost would be $15.

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable m and runs from negative 1 to 500. The y-axis of the plane represents the variable C and runs from negative 1 to 200. The line begins at the point (0,15) and goes through the point (400,143).

Exercise 4.5E.53

Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation S=400+0.15c models the relation between her weekly salary, S, in dollars and the amount of her sales, c, in dollars.

  1. Find Cherie’s salary for a week when her sales were 0.
  2. Find Cherie’s salary for a week when her sales were 3600.
  3. Interpret the slope and S-intercept of the equation.
  4. Graph the equation.
Exercise 4.5E.54

Patel’s weekly salary includes a base pay plus commission on his sales. The equation S=750+0.09c models the relation between his weekly salary, S, in dollars and the amount of his sales, c, in dollars.

  1. Find Patel’s salary for a week when his sales were 0.
  2. Find Patel’s salary for a week when his sales were 18,540.
  3. Interpret the slope and S-intercept of the equation.
  4. Graph the equation.
Answer
  1. $750
  2. $2418.60
  3. The slope, 0.09, means that Patel’s salary, S, increases by $0.09 for every $1 increase in his sales. The S-intercept means that when his sales are $0, his salary is $750.

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable w and runs from negative 1 to 20000. The y-axis of the plane represents the variable P and runs from negative 1 to 3000. The line begins at the point (0, 750) and goes through the point (18540, 2415).

Exercise 4.5E.55

Costa is planning a lunch banquet. The equation C=450+28g models the relation between the cost in dollars, C, of the banquet and the number of guests, g.

  1. Find the cost if the number of guests is 40.
  2. Find the cost if the number of guests is 80.
  3. Interpret the slope and C-intercept of the equation.
  4. Graph the equation.
Exercise 4.5E.56

Margie is planning a dinner banquet. The equation C=750+42g models the relation between the cost in dollars, C, of the banquet and the number of guests, g.

  1. Find the cost if the number of guests is 50.
  2. Find the cost if the number of guests is 100.
  3. Interpret the slope and C-intercept of the equation.
  4. Graph the equation.
Answer
  1. $2850
  2. $4950
  3. The slope, 42, means that the cost, C, increases by $42 for when the number of guests increases by 1. The C-intercept means that when the number of guests is 0, the cost would be $750.

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane represents the variable g and runs from negative 1 to 150. The y-axis of the plane represents the variable C and runs from negative 1 to 7000. The line begins at the point (0, 750) and goes through the point (100, 4950).

Use Slopes to Identify Parallel Lines

In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.

Exercise 4.5E.57

y=34x3;3x4y=2

Exercise 4.5E.58

y=23x1;2x3y=2

Answer

parallel

Exercise 4.5E.59

2x5y=3;y=25x+1

Exercise 4.5E.60

3x4y=2;y=34x3

Answer

parallel

Exercise 4.5E.61

2x4y=6;x2y=3

Exercise 4.5E.62

6x3y=9;2xy=3

Answer

not parallel

Exercise 4.5E.63

4x+2y=6;6x+3y=3

Exercise 4.5E.64

8x+6y=6;12x+9y=12

Answer

parallel

Exercise 4.5E.65

x=5;x=6

Exercise 4.5E.66

x=7;x=8

Answer

parallel

Exercise 4.5E.67

x=4;x=1

Exercise 4.5E.68

x=3;x=2

Answer

parallel

Exercise 4.5E.69

y=2;y=6

Exercise 4.5E.70

y=5;y=1

Answer

parallel

Exercise 4.5E.71

y=4;y=3

Exercise 4.5E.72

y=1;y=2

Answer

parallel

Exercise 4.5E.73

xy=2;2x2y=4

Exercise 4.5E.74

4x+4y=8;x+y=2

Answer

not parallel

Exercise 4.5E.75

x3y=6;2x6y=12

Exercise 4.5E.76

5x2y=11;5xy=7

Answer

not parallel

Exercise 4.5E.77

3x6y=12;6x3y=3

Exercise 4.5E.78

4x8y=16;x2y=4

Answer

not parallel

Exercise 4.5E.79

9x3y=6;3xy=2

Exercise 4.5E.80

x5y=10;5xy=10

Answer

not parallel

Exercise 4.5E.81

7x4y=8;4x+7y=14

Exercise 4.5E.82

9x5y=4;5x+9y=1

Answer

not parallel

Use Slopes to Identify Perpendicular Lines

In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.

Exercise 4.5E.83

3x2y=8;2x+3y=6

Exercise 4.5E.84

x4y=8;4x+y=2

Answer

perpendicular

Exercise 4.5E.85

2x+5y=3;5x2y=6

Exercise 4.5E.86

2x+3y=5;3x2y=7

Answer

perpendicular

Exercise 4.5E.87

3x2y=1;2x3y=2

Exercise 4.5E.88

3x4y=8;4x3y=6

Answer

not perpendicular

Exercise 4.5E.89

5x+2y=6;2x+5y=8

Exercise 4.5E.90

2x+4y=3;6x+3y=2

Answer

not perpendicular

Exercise 4.5E.91

4x2y=5;3x+6y=8

Exercise 4.5E.92

2x6y=4;12x+4y=9

Answer

perpendicular

Exercise 4.5E.93

6x4y=5;8x+12y=3

Exercise 4.5E.94

8x2y=7;3x+12y=9

Answer

perpendicular

Everyday Math

Exercise 4.5E.95

The equation C=59F17.8 can be used to convert temperatures, F, on the Fahrenheit scale to temperatures, C, on the Celsius scale.

  1. Explain what the slope of the equation means.
  2. Explain what the C-intercept of the equation means.
Exercise 4.5E.96

The equation n=4T160 is used to estimate the number of cricket chirps, n, in one minute based on the temperature in degrees Fahrenheit, T.

  1. Explain what the slope of the equation means.
  2. Explain what the n-intercept of the equation means. Is this a realistic situation?
Answer
  1. For every increase of one degree Fahrenheit, the number of chirps increases by four.
  2. There would be 160 chirps when the Fahrenheit temperature is 0°. (Notice that this does not make sense; this model cannot be used for all possible temperatures.)

Writing Exercises

Exercise 4.5E.97

Explain in your own words how to decide which method to use to graph a line.

Exercise 4.5E.98

Why are all horizontal lines parallel?

Answer

Answers will vary.

Self Check

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has eight rows and four columns. The first row is a header row and it labels each column. The first column is labeled "I can …", the second "Confidently", the third “With some help” and the last "No–I don’t get it". In the “I can…” column the next row reads “recognize the relation between the graph and the slope-intercept form of an equation of a line.” The third row reads “identify the Slope and y-intercept from an equation of a line”. The fourth row reads “graph a line using its slope and intercept”. The fifth row reads “choose the most convenient method to graph a line.” The sixth row reads “graph and interpret applications of slope-intercept”. The seventh row reads “use slopes to identify parallel lines” and the last row reads “use slopes to identify perpendicular lines.” The remaining columns are blank.

b. After looking at the checklist, do you think you are well-prepared for the next section? Why or why not?


This page titled 4.5E: Exercises is shared under a not declared license and was authored, remixed, and/or curated by OpenStax.

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