ALGEBRA UNIT 2



ALGEBRA UNIT 4

GRAPHING LINEAR FUNCTIONS

SLOPE/RATE OF CHANGE (DAY 1)

There are FOUR types of slope.

SLOPE/RATE OF CHANGE

Find the slope of the following using the Slope Formula:

1. (0, -2) & (2, 4) 2. (0, 3) & (4, 3) 3. (-2, 2) & (4, -1)

Find the slope of the following, using the [pic] method:

4. (2, 3) & (-4, -5) 5. (-5, 2) & (4, -3)

6. Find the average rate of change of the function shown to the right that represents the amount of money in a savings account Lender’s Bank?

|Week |Balance |

|1 |$128 |

|2 |$142 |

|3 |$156 |

|4 |$170 |

|5 |$184 |

7. Given the function [pic] find the rate of change in the interval [2,10].

8. Given the function graphed below. Find the average rate of change in the interval [pic]

9. Given the table of values below for a function, find the average rate of change of this function from t = -3 to t = 5.

|t |f(t) |

|-4 |6 |

|-3 |1 |

|-2 |-2 |

|-1 |-3 |

|0 |-2 |

|1 |1 |

|2 |6 |

|3 |13 |

|4 |22 |

|5 |33 |

GRAPHING LINEAR FUNCTIONS (DAY 2)

TYPES OF LINES/KEY FEATURES

|HORIZONTAL |VERTICAL |DIAGONAL (SLANTED) |

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|Parallel Lines | | |

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|Perpendicular Lines | | |

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HOW TO GRAPH LINEAR FUNCTIONS

|OPTION 1: No Graphing Calculator |OPTION 2: Graphing Calculator |

|Identify type of Line to be graphed |Put equation into graphing calculator. |

|Horizontal -- HOY (y = #) | |

|Vertical -- VUX (x = #) |Write down a table of values from calculator |

|Diagonal -- (y = mx + b) | |

|Make sure all equations are in y = mx + b before completing the following steps. |Plot points and connect with a line that ends with arrows. |

|Plot y-intercept (b#) on graph for starting point | |

|Create multiple points in both directions using the slope (m #) by doing [pic] |CALCULATOR STEPS: |

|Connect all points and put arrows on the end |Press y = button to input equation |

| |Input equation into y1 |

| |Press 2nd Graph to get a table of values |

1. Graph a line that has a slope of –1and goes

through the point (-1, 4).

2. Graph a line that goes through the point (3, 1) and

has a slope of [pic]

3. Graph: [pic]

4. Graph [pic]

5. Which is the equation of a line with a slope of -2 that passes through the point (-2, 0)?

(1) [pic] (2) [pic] (3) [pic] (4) [pic]

6. Which equation represents a line parallel to y = 2x + 5?

(1) y = -2x – 5 (2) y = 5x + 2 (3) y = 2x – 5 (4) y = -[pic]x – 5

7. Which equation represents a line perpendicular to 2y = -3x + 1?

(1) y = -[pic]x + 6 (2) y = [pic]x + 3 (3) y = [pic]x - [pic] (4) y = -[pic]x - [pic]

8. What is the equation of the line that has a y-intercept of –2 and is parallel to the line whose equation is 4y = 3x + 7?

(1) y = [pic]x – 2 (2) y = [pic]x + 2 (3) y = [pic]x – 2 (4) y = -[pic]x – 2

9. Write an equation of a line that is:

a) Parallel to the x-axis and 2 units above it.

b) Parallel to the y-axis and 2 units to the left of it.

c) Has undefined slope and passes through the point (3, -4).

d) Has a slope of 0 and passes through the point (-7, -8).

Write an equation for each of the graphed functions below using function notation.

10. 11. 12.

WRITING LINEAR FUNCTIONS (DAY 3)

|Slope – Intercept Form |Standard Form |

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|Written using Function Notation: |Written using Function Notation: |

1. Alex makes ceramic bowls to sell at a monthly craft fair in a nearby city. Every month, she spends $50 on materials for the bowls from a local art store. At the fair, she sells each completed bowl for a total of $25 including tax. Which equation expresses Alex’s profit as a function of the number of bowls that she sells in one month?

1) [pic] (3) [pic]

2) [pic] (4) [pic]

2. Which linear equation in point-slope form of the line contains the point (3,-2) and is perpendicular to the line [pic]

(1) [pic] (3) [pic]

(2) [pic] (4) [pic]

3. Samuel’s Car Service will charge a flat travel fee of $4.75 for anyone making a trip. They charge an additional set rate of $1.50 per mile that is traveled. Write an equation that represents the charges as a function C(m).

4. Veronica earned $150 at work this past week in her paycheck. She wants to buy some necklaces which cost $6 each. She writes a function to model the amount of money she will have left from her paycheck after purchasing a certain number of necklaces. She writes the function, [pic]. Determine what x and f(x) represent in the function.

5. Tim makes wooden salad bowls to sell at a monthly craft fair near his home town. Each month he spends $45 on specialty wood and other materials from his local lumber store. At the craft fair, Tim sells each completed salad bowl set for a total of $22, including tax. Express Tim’s profit as a function of the number of units that he sells.

6. Jonathan has been on a diet since January 2013. So far, he has been losing weight at a steady rate. Based on monthly weigh-ins, his weight, w, can be modeled by the function [pic], where m is the number of months after January 2013.

a) How much did Jonathan weigh at the start of the diet?

b) How much weight has Jonathan been losing each month?

c) How many months did it take Jonathan to lose 45 pounds?

7. The cost of operating Jelly’s Doughnuts is $1600 per week plus $.10 to make each doughnut.

a) Write a function C(d), to model the company’s weekly cost for producing d doughnuts.

b) What is the total weekly cost if the company produces 4,000 doughnuts?

c) Jelly’s Donuts makes a gross profit of $.60 for each donut they sell. If they sold all 4000 donuts they made, would they make money or lose money for the week? How much?

8. Andy graphed his wages and tips after several weeks of driving deliveries. Given the graph, write his earnings as a function of the number of deliveries that he made.

GRAPHING LINEAR INEQUALITIES (DAY 4)

STEPS:

1. Determine type of line to be graphed:

2. Identify Slope and y-interpret

3. Plot points (do not connect yet), then DETERMINE LINE TYPE

If the equation has a ____or ____ sign then you connect the points with a: _____________

If the equation has a _____ or______ sign then you connect the points with: ____________

Determine Shading by Picking a test point: (mark test point with an x on the graph)

• Shade where test point is ______________!!

Graph the following, label the solution area with a ‘S’, and identify a point in the solution.

1. y < 3 2. x [pic] 2

3. [pic] 4. [pic]

5. [pic] 6. x – 3y > -6

7. [pic] 8. [pic]

9. [pic] 10. [pic]

WRITING AND GRAPHING LINEAR EQUATIONS/INEQUALITIES (DAY 5)

Write an equation/inequality for each below and state a possible solution for each graph.

1. 2.

3. 4.

Graph the following: When appropriate label the solution area with a “S”

7. [pic] 8. [pic]

9. [pic] 10. [pic]

11. [pic] 12. [pic]

LINEAR FUNCTION APPLICATION PROBLEMS (DAY 6)

1. Shannon makes a weekly allowance of $25. She also makes $9.50 an hour at her job. Because of her age, Shannon can work no more than 20 hours a week.

a. Write a function for the amount of money she makes each week based on the amount of hours, h, she works.

b. What is the domain of the function for this situation?

c. Using the grid below, sketch a graph of the function over the domain you chose.

2. Olivia is going to a July 4th party and needs to bring an appetizer. She only has $50 to spend on the appetizer. She decides to take a cheese and cracker tray. One package of crackers cost $3.00 and the cheese costs $5 per pound.

Write a function to represent the amount of cheese and crackers Olivia can take in relation to the amount of money she has to spend.

Using the grid below, sketch a graph of the function and state one possible amount of cheese and crackers she could buy.

3. Sam’s profit after a year of selling custom bicycles that he has created can be represented by the function [pic]

|x |f(x) |

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|3 | |

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| |625 |

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|7 | |

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| |2575 |

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Complete the accompanying table that represents his profits from the past year.

In which month of the year did he begin to make a profit? Explain your answer.

4. Tina is looking to join a monthly coffee delivery club for the 10 months that she works. She found a coffee shop that offers this service for $40 startup fee and $8 per month.

Write an equation that represents the cost as a function C(m).

What is the domain of the function for this situation?

Using the grid below, sketch a graph of the function over the domain you chose.

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PROCEDURE TO FIND THE SLOPE (RATE OF CHANGE) OF A LINE WHEN GIVEN:

➢ 2 Points ---

or

➢ A graphed line ---

SLOPE SHOULD ALWAYS BE A ____________ IN ___________________.

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HOY y = #

VUX x = #

Diagonal y = mx + b

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PROCEDURE FOR APPLICATION WP:

• Read problem carefully - Highlight IMPORTANT-KEY WORDS/information

• Determine if word problem represents a:

• Linear Equation (= sign) –only 1 answer

• Linear Inequality [pic] signs- --multiple solutions (shading required)

• Determine correct Axes for graph depending on the domain

▪ L shaped axes – no negative x #’s allowed in domain

▪ t shaped axes – all x #’s allowed in domain

[pic]

[pic]

[pic]

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