Math 3 Unit 2 Homework PacketHomework 2-1

Discovering how parts of linear equations make lines parallel or perpendicular.

1. Inspect the graph and determine the following:

(a) Which pairs of equations produce parallel

lines? _________________ & _________________

(b) Which pairs of equations produce perpendicular

lines? _________________ & _________________

2. State the slope and the coordinates of the y-intercept.

(a) y = 2x + 3 m = _________; b = _______________

(b) y = –2x + 7 m = _________; b = _______________

3. By comparing equations, how can you tell if lines will be parallel? What about perpendicular? (Hint: look at the parts

of a linear equation: y = mx + b.)

__________________________________________________________________________________________________

__________________________________________________________________________________________________

4. Find the slope of a line parallel to each of the lines below:

(a) y = 3x + 8 (b) y = 2x – 7 (c) y =13 x +

m = _______ m = _______ m = ________

5. Find the gradient of a slope perpendicular to each of the lines below:

(a) y = 3x + 8 (b) y = 2x – 7 (c) y =13 x + 8

m = _______ m = _______ m = ________

6. Determine the equation of the line that is parallel to the given line and passes through the given point:

(a) y = 2x + 7 (b) y = 3x – 1 (c) y =6x + 2

A(2,9) B(2,12) C(9,8)

7. Determine the equation of the line that is perpendicular to the given line and passes through the given point:

(a) y = 2x + 7 (b) y = 3x – 1 (c) y =6x + 2

A(1,9) B(2,12) C(9,8)

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Homework 2-2

1. A car enters an interstate highway 15 miles north of the city. The car travels due north at an average speed of 30 miles per hour. Write an equation to model the car’s distance d from the city after traveling for h hours. Graph the equation

2. A tree 5 feet tall grows an average of 8 inches each year. Write and graph an equation to model the tree’s height h after x years.

Find a linear model and use it to make a prediction3. There are 2 leaves along 3 inches of an ivy vine. There are 14 leaves along 15 inches of the same vine. How

many leaves are there along 6 inches of the vine?

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4. The table below shows the average energy requirements for male children and adolescents. a. Graph the data. Use linear regression to model the data with a linear equationb. Estimate the daily energy requirements for a male 16 year old.c. Do you think the model also applies to adult males? Explain.

5. Graph 5x – 2y > - 10 on the coordinate plane.

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Age (years) Energy Needed (Calories)

1 11002 13005 18008 220011 250014 280017 3000

Homework 2-3

Solve each system by graphing. Check your results.1. y = x – 2 2. -5x + y = -9

y = -2x + 7 x + 3y = 21

Solve each system by substitution. Check your results.

3. 3x – 2y = 8 4. 2x + 8y = 64y = 6x – 5 x = -4y + 3

Solve Each system of equations by elimination. Check your results.5. -6y + 18 = 12x 6. x + 4y = 12

3y + 6x = 9 -x -2y = -6

Determine whether each system is dependent, independent, or inconsistent.

6. y = 4x + 5 8. 3x -2y = 18 9. x – 4y = 173y – 12x = 15 15x = 10y -21 2x – 5y = 12

10. You want to bake at least 6 and at most 11 loaves of bread for a bake sale. You want at least twice as many loaves of banana bread as nut bread. Write and graph a system of inequalities to model the situation.

11. A psychologist needs at least 40 subjects for her experiment. She cannot use more than 30 children. Write and graph a system of inequalities.

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Homework 2-4

4. 5.

5

6. 7.

8. 9.

Homework 2-5

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12*. A biologist is developing two new strains of bacteria. Each sample of Type I bacteria produces four new viable bacteria, and each sample of Type II produces three new viable bacteria. Altogether, at least 240 new viable bacteria must be produced. At least 30, but not more than 60, of the original samples must be Type I. Not more than 70 can be Type II. A sample of Type I costs $5 and a sample of Type II costs $7. How many samples of Type II bacteria should be used to minimize cost?

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Variables:

x =

y =

Objective Function: Constraints: Computation Box:

Variables:

x =

y =

Objective Function: Constraints: Computation Box:

Homework 2-6

1. If the first term of an arithmetic sequence is 5 and the common difference is -2, find the next four terms.

2. If I know that the first term of the arithmetic sequence is -2 and the fifth term is 6, find the second, third, and fourth terms in the sequence.

3. If the first term of an arithmetic sequence is -25 and the third term is 14, find the second term.

4. If the first term of an arithmetic sequence is 15 and the third term is 65, find the second term.

Is the given sequence arithmetic? If so state the common difference

5. 12, 15, 18

6. 100, 110, 130

7. -2, -1, 0

8. 123, 221, 319

Homework 2-7

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Variables:

x =

y =

Objective Function: Constraints:

Given the recursive equation for each arithmetic sequence, write the explicit equation.

3. f(n) = f(n – 1) – 2; f(1) = 8

4. f(n) = 5 + f(n – 1); f(1) = 0

5. Find the 125th term of the sequence 5, 11, 17, 23, …

6. Abbie decides to start doing crunches as part of her daily workout. She decides to do 15 crunches the first day and then increase the number by 4 each day after that. Write an explicit formula for the number of crunches Abbie will do on day n. How many crunches would she do on day 25?

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2.

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7. You are trying to save money for an xbox one. You currently have $50 and save an additional $12 every week. Write the recursive and explicit formula for this arithmetic sequence and find how much money you will have after 12 weeks?

8. Amelia is tracking her mathematics test scores. She starts out slow, but continues to get better with each test. Her first test was a 75. Her second was a 78, and third was an 81. If this trend continues, what would her score on the 10th test be?

9. A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on in the same increasing pattern. If the theater has 20 rows of seats, how many seats are in the 20th row of the theater?

Homework 2-8

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1.

a. Fill in the rest of the table.b. Graph the sequence.

c. How is the common difference related to the graph?

d. Use the graph to find the y-intercept

e. How can you calculate the y-intercept of the sequence without having to graph it first?

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2.

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