Module: Linear Equations



Name ________________________________________ HW 6-1

Which ordered pairs are solutions of each equation?

1. y = 3x + 1 a. (0, 1) b. (1/3, 2) c. (-1, -2/3) d. (-1, -2)

2. 2a = 5 – b a. (5, 0) b. (5, -5) c. (5/2, 0) d. (1, -3)

Solve each equation if the domain is {-4, -2, 0, 2, 4}. Make a t-table!!

3. x + y = 4 4. y = -4x + 6 5. 4x + 8 = 2y

Make a table and GRAPH the solution set.

6. y = 2x + 1 7. 2x – 3y = 6

Solve the following equations for y.

8. 2x + 5y = 3 9. 3x + y = 8 10. 4x – 5y = 8

Name _______________________________________ HW 6-2

Without a calculator, graph each of the following on the graph paper provided.

1. f(x) = 2x - 7

|x | |f(x) |

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2. f(x) = -3x + 4

|x | |f(x) |

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Solve each equation for y and then graph each equation.

3. 6x + 7 = -14y

|x | |y |

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4. 8x - y = 16

|x | |y |

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Name_______________________________ HW 6-3

Slope

Graph each pair of points and draw a line that contains both points.

1. A(1, 4), B(-2, 2)

2. M(0, -1), N(-3, 1)

3. X(2, 3), Y(3, -1)

4. In your own words, explain slope._______________________

_____________________________________________________

_____________________________________________________

Given the following information about two wheelchair ramps:

a) it gains 70 feet of altitude for every 900 feet it travels horizontally

b) it gains 65 feet of altitude for every 825 feet it travels horizontally

5. Which wheelchair ramp is steeper? Explain your answer._______________________

_______________________________________________________________________

_______________________________________________________________________

6. Match each stair step diagram with the ratio of measures (vertical/horizontal) that best describes the diagram.

a. 3/3 _____ b. 3/2 _____ c. 2/3 _____ d. 6/5 _____ e. 1/3 _____ f. 3/1 _____

I.[pic] II.[pic] III.[pic] IV.[pic] V.[pic] VI.[pic]

7. Make a sketch of stair steps with the given steepness. The steepness (ratio) is vertical measure (rise) compared to horizontal measure (run).

a. 2/1 b. 1/2 c. -2/1 d. 1/-2 e. 0/-2 f. 1/0

[pic] [pic] [pic] [pic] [pic] [pic]

8. For each of the sketches above, describe whether the steps are increasing, decreasing, horizontal, or vertical.

a. 2/1 b. 1/2 c. -2/1 d. 1/-2 e. 0/-2 f. 1/0

___________ ___________ ___________ ___________ ___________ ___________

Lesson 1: Finding Slope HW 6-4

Homework

Find the slope of the line through the given points.

1. (-1, 2) and (-5,10) 2. (-7, 10 ) and (1, 10)

3. (1,3) and (0,-9) 4. (3, 7) and (3, -8)

5. (-3,7) and (-3, 6) 6. (100, 10) and (-3, 50)

7. (18, 6) and (-7, 7) 8. [pic] and [pic]

9. (0, 1) and (4, 0) 10. (5x, y) and (2x, 2y)

Find the slope of the following:

11. 12.

Name Date

In Exercises 1 and 2, describe the slope of the line. Then find the slope.

1. 2.

In Exercises 3 and 4, the points represented by the table lie on a line. Find the slope of the line.

3. 4.

In Exercises 5–8, find the slope and the y-intercept of the graph of the linear equation.

5. [pic] 6. [pic]

7. [pic] 8. [pic]

In Exercises 9–12, graph the linear equation. Identify the x-intercept.

9. [pic] 10. [pic]

11. [pic] 12. [pic]

In Exercises 13 and 14, graph the function with the given description. Identify the slope, y-intercept, and x-intercept of the graph.

13. A linear function f models a relationship in which the dependent variable decreases 3 units for every 2 units the independent variable increases. The

value of the function at 0 is 5.

14. A linear function g models a relationship in which the dependent variable increases 2 units for every 7 units the independent variable increases. The

value of the function at 0 is (1.

Name HW 6-6

In Exercises 1 and 2, describe the slope of the line. Then find the slope.

1. 2.

In Exercises 3 and 4, the points represented by the table lie on a line. Find the slope of the line.

3. 4.

In Exercises 5–8, find the slope and the y-intercept of the graph of the linear equation.

5. [pic] 6. [pic]

7. [pic] 8. [pic]

In Exercises 9–12, graph the linear equation. Identify the x-intercept.

9. [pic] 10. [pic]

11. [pic] 12. [pic]

13. A linear function g models the growth of your hair. On average, the length of a hair strand increases 1.25 centimeters every month.

a. Graph g when [pic].

b. Identify the slope and interpret the y-intercept of the graph.

c. By how much, in inches, does the length of a hair strand increase each month?

HW 6-7

Graphing 3 ways Name

HW 6-8

Graph each of the following equations on the graph below and label the equation. Check your answer with a graphing calculator.

1. Graph using y = mx + b.

a) y = 3x - 4

m = b =

b) y = x + 1

m = b =

c) y = -2x + 2

m = b =

d) y = -x - 3

m = b =

2. Graph using x- and y-intercepts.

a) 2x + 3y = 6

x-int: y-int:

b) x - 2y = -8

x-int: y-int:

c) -3x + y = -3

x-int: y-int:

d) -4x - 2y = 6

x-int: y-int:

3. Graph using a table.

a) y = 2x – 1 b) 2x + y = 4

Graphing Inequalities Name HW 6-9

Graph each inequality. Solve for y when necessary!!

Remember, if the graph is y > __, shade up and use a dotted line (≥ uses a solid line).

If the graph is y < __, shade down and use a dotted line (≤ uses a solid line).

1. y ≤ 3 - 2x

|x | |y |

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2. x + y > 1

|x | |y |

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3. y ≥ x - 1

|x | |y |

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4. y ≤ 3x - 1

|x | |y |

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Name HW 6-10

In words, describe the solutions of the inequality.

1. [pic] 2. [pic]

Tell whether the ordered pair is a solution of the inequality.

3. [pic] 4. [pic]

5. [pic] 6. [pic]

Tell whether the ordered pair is a solution of the inequality whose

graph is shown.

7. [pic] 8. [pic]

9. [pic] 10. [pic]

11. You must sell at least $75 worth of concert tickets to qualify for the

band trip. Floor seat tickets are $15 each and balcony seat tickets are

$5 each. Write an inequality for the number of tickets you must sell.

If you sell 3 floor seat tickets and 4 balcony seat tickets, will you qualify for the band trip?

Graph the inequality in a coordinate plane.

12. [pic] 13. [pic] 14. [pic]

15. [pic] 16. [pic] 17. [pic]

18. You have $12 to spend on fishing equipment. Hooks cost $0.50 each and sinkers cost $0.35 each.

a. Write and graph an inequality that represents the numbers of hooks you can buy and sinkers you can buy.

b. Identify and interpret two solutions of the inequality.

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Homework 6-5

|x |0 |2 |5 |7 |

|y |3 |3 |3 |3 |

|x |(2 |1 |4 |7 |

|y |0 |1 |2 |3 |

|x |3 |1 |(1 |(3 |

|y |(4 |1 |6 |11 |

|x |4 |4 |4 |4 |

|y |(2 |1 |4 |7 |

X

Y

X

Y

X

Y

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