Algebra Unit 5 – Graphing Linear Equations

Date Topic HW

F – 11/1 Graphing Linear Equations

HW #1 (p. 5 – 6)

M – 11/4 Graphing Linear Equations

HW #2(p. 10-11)

W – 11/6 Graphing Linear Equations Word

Problems

HW #3(p. 17-19)

Th – 11/7 Quiz/Horizontal/Vertical Lines

HW #4(p. 22-23)

F – 11/8 Graphing Systems of Linear Equations

HW #5(p. 26-27)

T – 11/12 Rate of Change/Slope HW #6(p. 31)

W – 11/13 Writing the equation of a line

HW #7(p. 34)

Th – 11/14 Writing the equation of a line

HW #8(p. 37-38)

F – 11/15 Parallel and Perpendicular Lines

HW #9(p. 43-44)

M – 11/18 Review Study for Test

T – 11/19 Test

Lesson #1: Graphing Linear Equations

METHOD 1 – USING A TABLE OF VALUES (from your graphing calculator!)

1. y = -3x + 1

2. y = 2x – 7

METHOD 2 – SLOPE-INTERCEPT FORM

Observations:

Coefficient of x:

As the coefficient of x increases, the line ___________________________________________

As the coefficient of x decreases, the line __________________________________________

If the coefficient of x is positive, then the line ________________________________________from left to right.

If the coefficient of x is negative, then the line________________________________________from left to right.

Constant:

As the constant number in the equation changes, the line ______________________________

The constant number is the number at which the line __________________________________

____________________________________________________________________________

Slope-Intercept Form:

Steps for Graphing Linear Equations Using Slope-Intercept Method:1. Plot the y-intercept on the y-axis. (b for “begin”)2. Write the slope as a fraction and use this fraction to determine other points on the line. The numerator represents the vertical change and the denominator represents the horizontal change. (m for “move”) 3. Connect the points using a straight line. Be sure to use arrows and label with the equation.

Graph each of the following linear equations using the slope-intercept method.

1. y = 2x + 4

2. y = 3x – 5

3. y = -4x + 1

4. y = -3x

5. y = x + 2

6. y = -x – 6

7. y = ½ x + 2

8. y = 2/3 x – 4

9. y = - ¾ x + 3

HW #1: Graphing Linear Equations

Complete each table of values. Then graph the equation.

1. y = 2x – 5 2. y = -2x + 1

3. y = -x + 3 4. y = 14 x – 2

5. y = 2x – 5 6. y = -3x + 1m = ______ m = ______b = ______ b = ______

7. y = x – 6 8. y = 23 x + 1

m = ______ m = ______b = ______ b = ______

9. On the set of axes below, draw the graph of the equation y=−34

x+3.

Is the point (3,2) a solution to the equation? Explain your answer based on the graph drawn.

Lesson #2: Slope-Intercept Form

An equation that is in slope-intercept form follows this format

y = mx + b

slope y-intercept

Which function has the same y-intercept as the graph below?

1)

2)3)4)

Rewrite each equation in slope-intercept form.

1. y - 3x = 5 2. 3y = 6x - 12

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

5. x - y = 7 6. -4x - y = 1

7. -x + 2y = 6 8. 3x + 2y - 6 = 0

9. 5x + 2y = 10 10. 8y - 4x = 16

11. -2x + 3y = -12 12. 8x - 2y = 2

13. y + 4x = 6

14. 2y - 6x = 8

15. x + 2y = -4

16. 4y = 3x + 12

17. The graph of the equation intersects the y-axis at the point whose coordinates are1)2)3)4)

18. The value of the x-intercept for the graph of is1) 102)

3)

4)

Lesson #3: Real World Linear Equations

1. John was approved for a car loan with 0% interest rate as long as the balance is paid off in twelve months. The graph represents John’s payment plan to ensure that he doesn’t have to pay interest.

a. How much did John borrow?

b. How much is he paying off on the loan each month?

c. How long would it take John to pay off the loan if he doubled his monthly payment?

d. Ignoring any interest, how long would it take John to pay off the loan if he cut his payments in half?

e. For the original loan, what is John’s loan balance eight months into paying off the loan?

f. Write an equation that represents John’s payment plan using “y” for the loan balance and “x” for the months.

2. Your parents want to throw you a party for your graduation. They have decided to hire a band for $500 and figure about $15 per person for food and drink. Write an equation to describe the situation. Then graph the equation on the grid provided. Be sure to label all parts of the graph. Use the graph and the equation to determine the cost of inviting 50 people.

3. Use the graph below to answer the questions.

a. How many pies must Sally sell in one day to break even?

b. If Sally has made a profit of $15, how many pies has she sold?

c. How much profit does Sally make on each pie?

Profit in Dollars

Number of Pies Sold

50 1510

403020100

-10-20-30

Sally's Pie Shop Daily Profit

d. What does the –intercept of -30 mean?

e. If Sally sells 50 pies in one day, what will be her profit?

4. A deluxe phone company charges a $200 flat fee in addition to its hourly rate of $100 per hour. (This is a special phone company that offers unprecedented James Bond-like technology, which is why the company can charge so much.)

Use the blank graph below to draw a graph of this company’s rate for an entire year.

5. Jasmine has $300 in her bank account and each week she spends $50. Which graph represents the relationship between the amount remaining in the bank, A, after weeks, w, represented by the equation 300 – 50w = A?

A) B) C) D)

6. Shawn has $575 in the bank and each week he withdraws $25 out of his account. After how many weeks will he have only $100 left in the bank?

A) 15 weeksB) 3 weeks C) 19 weeksD) 27 weeks

7. Hannah types at a rate of 50 words per minute. At this rate how many minutes will it take her to type a 200 word paper?

A) 4 minutesB) 0.25 minutesC) 4 wordsD) 0.25 words

8. A fish tank has a volume of 520 in3. It is emptied at a constant rate of 10 cubic inches every minute. Which equation represents the volume v, after t, time in minutes?

A) v = 10t – 520B) v = 10t + 520 C) v = 520 – 10t D) v = -520 – 10t

9. Melissa wants the city to provide every Farrington classroom with recycling bins and is in the process of collecting student signatures for her petition. So far Melissa has collected 82 signatures and wants to collect 15 signatures for each classroom she visits during advisory time. If S is the total number of signatures Melissa has collected, and C is the number of classroom visited, write an equation.

10. Julie is a waitress and earns $5 for every hour she works. If h is the number of hours she works and p is her total pay, which table represents this relationship: P = 5h

Hours

Pay $

0 $01 $52 $103 $15

Hours

Pay $

0 $51 $102 $153 $20

Hours

Pay $

0 $51 $152 $253 $35

Hours

Pay $

0 $01 $102 $203 $30

13. The state department of transportation recently filled the road salt storage building on the highway near your house with 2400 tons of road salt. A truck can hold 12 tons of road salt in one load. You can represent this relationship with the equation y = 2400 – 12x, where y is the amount of road salt left in the storage building and x is the number of truck loads of salt. Complete the table below to demonstrate this relationship.

0

15

30

45

HW #3 – Graphing Linear Equation Word Problems

1. So far the school has already raised $550 for prom. Each senior is required to sell $25 in chocolate bars to help cover the additional costs of prom. The equation that represents this situation is A = 550 + 25s, where s is the number of seniors selling chocolate bars and A is the total amount raised for prom.

A) Fill out the table. B) Make a graph.

0

5

10

15

2. Super Painters charges $1.00 per square foot plus an additional fee of $25.00 to paint a living room. If x represents the area of the walls of Francesca's living room, in square feet, and y represents the cost, in dollars, which graph best represents the cost of painting her living room?

1)

2)

3)

4)

3. The gas tank in a car holds a total of 16 gallons of gas. The car travels 75 miles on 4 gallons of gas. If the gas tank is full at the beginning of a trip, which graph represents the rate of change in the amount of gas in the tank?1)

2)

3)

4)

4. The graph below was created by an employee at a gas station.

Which statement can be justified by using the graph?1) If 10 gallons of gas was purchased, $35 was

paid.2) For every gallon of gas purchased, $3.75

was paid.3) For every 2 gallons of gas purchased, $5.00

was paid.4) If zero gallons of gas were purchased, zero

miles were driven.

5. Max purchased a box of green tea mints. The nutrition label on the box stated that a serving of three mints contains a total of 10 Calories. On the axes below, graph the function, C, where represents the number of Calories in x mints.

Write an equation that represents . A full box of mints contains 180 Calories. Use the equation to determine the total number of mints in the box.

6. Zeke and six of his friends are going to a baseball game. Their combined money totals $28.50. At the game, hot dogs cost $1.25 each, hamburgers cost $2.50 each, and sodas cost $0.50 each. Each person buys one soda. They spend all $28.50 on food and soda. Write an equation that can determine the number of hot dogs, x, and hamburgers, y, Zeke and his friends can buy. Graph your equation on the grid below.

Determine how many different combinations, including those combinations containing zero, of hot dogs and hamburgers Zeke and his friends can buy, spending all $28.50. Explain your answer.

Lesson #6: Slope Formula & Rate of Change

3 Versions of the Slope Formula

FORMULA Best Used When Given…

Slope = riserun

m = ∆ y∆ x

m = y2− y1

x2−x1

Examples: Find the slope.

1. 2. 3. A(-3, -2) and B(5, 4)

Find the rate of change.

4. 5.

6.

x

y

x

y

Cost ($)

Temperature (°F)

Hours After Storm108642

1 2 3 4 5 6 7 8 9 10Number of Magazines

21181512963

O

908070605040302010

O

8.7.

Sales ($)

Altitude (ft.

Day106 842 1086420 0x x

20 1,000

40 2,000

60 3,000

80 4,000

100 5,000y y Book Sales

Hawk Diving Toward Prey

9. 10.

Lesson #9: Graphing Parallel & Perpendicular Lines

Parallel Lines: two lines in the same plane that do not intersect

____________________________________________________

____________________________________________________

Practice: Are the twolines parallel? Explain.

1. y = 3x + 7 and y = 3x – 8 YES or NO

2. y = 23x – 2 and y =

32x + 1 YES or NO

3. y = -2x + 4 and 6x + 3y = 12 YES or NO

4. Name any three lines that are parallel to the line y = -x + 4.

5. On the graph below, which two lines are parallel?

a b c

To finding the equation of a new line that is PARALLEL to the original line and passes through a given point:

SLOPE of New Line: _________________________________________

EQUATION of New Line: ___________________________________

Practice without using a graph!

6. Find the equation of the line that is parallel to y = 2x + 6 and passes through the point (-1, 10).

7. Find the equation of the line that is parallel to 3x + y = 7 and passes through the point (-2, -9).

8. Find the equation of the line that is parallel to x = 2y – 1 and passes through the point (4, 4).

9. Find the equation of the line that is parallel to 5x – y = 0 and passes through the point (0, 8).

Perpendicular Lines: two lines in the same plane that intersect at right angles

____________________________________________________

____________________________________________________

Practice: Are the twolines parallel? Explain.

1. y = 3x + 7 and y = -3x – 8 YES or NO

2. y = 23x – 2 and y =

32x + 1 YES or NO

3. y = -2x + 4 and y = 12x + 5 YES or NO

4. Name any three lines that are perpendicular to the line y = -x + 4.

5. Graph the lines y = -3x + 1 and y = 13x + 1 to demonstrate that they are perpendicular.

To finding the equation of a new line that is PERPENDICULAR to the original line and passes through a given point:

SLOPE of New Line: _________________________________________

EQUATION of New Line: ___________________________________

Practice without using a graph!

6. Find the equation of the line that is perpendicular to y = 2x + 6 and passes through the point (-2, 4).

7. Find the equation of the line that is perpendicular to 3x + y = 7 and passes through the point (-6, 0).

8. Find the equation of the line that is perpendicular to x = 2y – 5 and passes through the point (4, 4).

9. Find the equation of the line that is perpendicular to 5x – y = 0 and passes through the point (0, 8).