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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 run

rise method:

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

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 ___________________.

x

y

x

y

2

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 $148

7. Given the function 5x3x)x(f 2 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 0x3

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

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GRAPHING LINEAR FUNCTIONS (DAY 2)

TYPES OF LINES/KEY FEATURES HORIZONTAL VERTICAL DIAGONAL (SLANTED)

HOW TO GRAPH LINEAR FUNCTIONS OPTION 1: No Graphing Calculator OPTION 2: Graphing Calculator

Identify type of Line to be graphed

Horizontal -- HOY (y = #)

Vertical -- VUX (x = #)

Diagonal -- (y = mx + b)

Make sure all equations are in y = mx + b

before completing the following steps.

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

point

Create multiple points in both directions

using the slope (m #) by doing run

rise

Connect all points and put arrows on the

end

Put equation into graphing calculator.

Write down a table of values from

calculator

Plot points and connect with a line

that ends with arrows.

CALCULATOR STEPS:

Press y = button to input equation

Input equation into y1

Press 2nd Graph to get a table of

values

Parallel Lines

Perpendicular Lines

x

y

x

y

x

y

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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 3

2

3. Graph: 4x6y2

4. Graph 21x4y3

x

y

x

y

x

y

x

y

5

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

(1) 4x2y (2) 4x2y (3) x22y (4) 2x4y

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 = -2

1x – 5

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

(1) y = -3

2x + 6 (2) y =

3

2x + 3 (3) y =

2

3x -

2

1 (4) y = -

3

2x -

2

1

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 = 4

3x – 2 (2) y =

4

3x + 2 (3) y =

3

4x – 2 (4) y = -

3

4x – 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.

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WRITING LINEAR FUNCTIONS (DAY 3)

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) 25x50)x(p (3) 25x15)x(p

(2) 50x25)x(p (4) x25)x(p

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

perpendicular to the line 6x3y2

(1) 2x3

22y (3) 2x

3

2y

(2) 2x3

22y (4) 3x22y

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, x6150)x(f . 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.

Slope – Intercept Form Standard Form

Written using Function Notation:

Written using Function Notation:

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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 205m3w , 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 Doughnuts makes a gross profit of $.60 for each doughnut they sell. If they

sold all 4000 doughnuts 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.

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x

y

x

y

x

y

x

y

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 2

3. 2x3y 4. 4x4y2

HOY y = #

VUX x = #

Diagonal y = mx + b

9

x

y

x

y

x

y

x

y

x

y

x

y

5. 7x4y2 6. x – 3y > -6

7. 3

4xy

3

2 8. x

5

13y

5

3

9. 42

xy 10. x38y4

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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.

x

y

x

y

x

y

x

y

11

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

7. x3

24y 8. 06y

9. 9xy3 10. 16y4x5

11. 4y7

4x

7

3 12. 12y4x6

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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.

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 },,,{ 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

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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 1000x325)x(f

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.

x f(x)

3

625

7

2575

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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.

5.