Ch 4 Notes Alg 1H 1

Chapter 4 Class Notes Alg. 1H

4-A1 (Lesson 4-1)“Rate of Change and Slope” p. 187-191

Slope is the Rate of Change: the ___________ of the vertical __________

(change in _____) to the horizontal _________ (change in _____) between any two

points on a line.

Slope = = =

Constant:

Not constant:

Ex. 1:

Ex. 2:

Positive Negative

Zero

Undefined

Ch 4 Notes Alg 1H 2

3A) (3, 6) (4, 8) B) (-4, 2) (2, 10)

4A) (-2, 2) (-6, 4) B) (4, 3) (-1, 11)

5A) (6, 7) (-2, 7) B) (-4, -2) (0, -2)

6A) (3, 2) (3, -1) B) (-2, -1) (-2, 5)

Find coordinates when given the slope: Set up a ______________________ with the

slope formula on one side and the given slope on the other. Solve using

_________________ _________________________.

7A) (1, 4) (-1, r) m = 2 B) (r, -6) (5, -8) m = -8

C) (9, r) (6, 3) m = 1

3

Ch 4 Notes Alg 1H 3

4-A2 (Lesson 4-3) “Slope-Intercept Form” p. 204-206

Slope-intercept form:

Ex. 1-2:

Ex. 3: A) 2 3y x C) 4 3 12x y D) 2 3 6x y

B) 1

54

y x

Ex. 4: Profit = _______________ - _______________

The band is selling sandwiches for $5 each. The cost of

ingredients and supplies is $350.

A. Equation B. Graph

C. Find the profit on 168 sandwiches.

D. How many sandwiches must they sell to make

a profit of $700?

-1 x

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-1 x

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Ch 4 Notes Alg 1H 4

4-A3 (Lesson 4-4) “Writing Equations” p. 213-216

When given the Slope and 1 Point:

Use the ____________________________ form:

Find the y-intercept: replace ____ with the slope and replace x and y

with the coordinates of the _____________ that is given.

Ex. 1: m = -1; (-4, 7)

When given 2 Points:

First find the slope: use the __________ ________________

Use the ____________________________ form:

Find the y-intercept: replace _____ with the slope and __ and ___ with

the coordinates of ___________ point that is given.

Ex. 2: (-1, 12); (4, -8)

p. 216 Check Your Understanding (#1-7 odds)

1. (4, -2); m = 2 3. (-3, 5); m = -1 (graph # 3)

5. (6, 0) (0, 4) 7. (-5, 2) (0, 7)

Ex. 3: Ex. 4:

-1 x

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Ch 4 Notes Alg 1H 5

p. 216 Check Your Understanding (#8-9)

Ch 4 Notes Alg 1H 6

4-A5 (Lesson HEATH 5.5) “Standard Form of a Linear Equation”p. 264-266

& Power Point

Standard Form: Ax By C

Variable terms on ___________, x-term first and constant on the _________

__________ coefficients (A, B, C) (no _______________ or ______________)

Positive ____________ coefficient (A)

Coefficients have _______________________.

Refer to Example 1 in your Heath book.

1. 3

24

y x 2. 5

38

y x

Refer to Example 2 in your Heath book.

3. 0.23 5.2y x 4. 1.5 3 1.25y x

5. 2 1

35 3

y x

POWER POINT

Ex. 1:

23

5y x Ex. 2: 0.55 1.35y x Ex. 3:

1(6,8)

3m

Ch 4 Notes Alg 1H 7

Ex. 4: Candy corn costs $2 per pound at the candy store and M&Ms cost $3 per pound. With

$30 to spend, what are the different amounts of the two candies that you can buy?

Ex. 5: You are running for class president and have $48 to spend on publicity for your

campaign. It costs $2 to make a campaign button and $1.20 to make a poster. Write an equation

that represents the different numbers of buttons, x, and posters, y, that you could make.

Ex. 6: Dogs sell for $50 and cats sell for $30 at Pets-R-Us. Sales figures for the busy holiday

shopping season showed that the store received $3300 total for dog and cat sales in one weekend.

Write an equation to describe the sales that weekend of dogs, x, and cats, y.

Ch 4 Notes Alg 1H 8

4-A7 (Lesson 4-5) “Writing Equations in Point-Slope Form” p. 219-222

Point-Slope Form:

1) (1, -4) m = 8

3

2) point: ___________ point: ___________

m = _______

3) (-4, 4) m = _______

Linear Equations:

Standard Form:

Point-Slope Form:

Slope-Intercept Form:

4) 1 7 5y x 5) 6 3 4y x

Ch 4 Notes Alg 1H 9

6) Sketch:

Concept Summary:

If you are NOT given the slope, but you are given TWO POINTS:

Use the ____________ _______________ to find the slope.

Choose _______________ of the 2 points.

Now you know the slope and one point.

p. 222-223 Check Your Understanding (#1-13)

Given the Slope and One Point

Use Slope-Intercept Form Use Point-Slope Form

Write the final equation in the form specified in the directions.

If not specified, use the Slope-Intercept Form.

-1 x

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Ch 4 Notes Alg 1H 10

4-A8 Problem Solving Using Linear Equations Power Point Notes (Heath 5.7) Alg 1H

Ex. 1&2) Type of Problem: ____________________________

1. A stereo sales person is paid a base salary of $500 per month plus 7% commission on the amount of stereo equipment he sells each month. Write a linear model that shows his salary, y, in terms of the amount of his sales, x, each month. Use the equation to predict how much his November paycheck will be if he sells $35,000 worth of equipment that month.

2. A photographer charges $50 for a sitting and a basic package of photos. Additional 5 x 7 pictures cost $12 each. Write a linear equation which gives the total cost in dollars, y, in terms of how many extra 5 x 7 pictures you purchase, x.

Ex. 3&4) Type of Problem: ____________________________

3. Between 1990 and 2005 the amount spent on advertising by the Locktite company increased by approximately $480 per year. In 1996 the company spent $12,000 on advertising. Find an equation that gives the total amount spent on advertising, A, in terms of the year, t. Let t = 0 correspond to the year 1990. Find the amount that was spent in 2002.

4. Between 2000 and 2010, the monthly rent for a one-bedroom apartment increased by $20 per year. In 2007, the rent was $350 a month. Find an equation that gives the monthly rent in dollars, y, in terms of the year, t. Let t = 0 correspond to 2000.

Ch 4 Notes Alg 1H 11

Ex. 5&6) Type of Problem: ____________________________

5. On January 1, Spike had a savings account balance of $2742. By April 1, his balance had increased to $3597. Write a linear equation showing the amount in his account, A, in terms of the month, t. Think of the months numbered with January as month 1 and April as month 4. What will the account balance be by August if it continues to increase at the same rate?

6. The population of Laredo, Texas, was about 197,000 in 2003. It was about 123,000 in 1990. Write a linear equation to describe the changes in the population, P, in terms of the year, x. Let x = 0 correspond the year 1990. Round the slope to the nearest whole number.

Ex. 7&8) Type of Problem: ____________________________

7. A fruit stand at the Farmer’s Market is selling Granny Smith apples for $4 a pound and blackberries for $6 a pound. Write a linear equation showing the possible number of pounds of apples, a, and pounds of blackberries, b, that were sold on Thursday if total sales for the day were $336. Use the equation to find the # of pounds of blackberries sold if 10 pounds of apples were sold.

8. Grandma Williams made 240 oz. of jelly. She used to different types of jars for the jelly. The first type held 10 oz. and the second type held 12 oz. Write an equation that represents the different numbers of 10 oz. jars, x, and 12 oz. jars, y, that will hold all of the jelly.

Ch 4 Notes Alg 1H 12

4-A9 (Lesson 4-7) “Geometry: Parallel and Perpendicular Lines” p. 236-239

Parallel Lines: lines in the same ___________ that never _________________; two nonvertical

lines that have the same _________________ and different ________________. any two

___________________ lines.

1) through (4, -1) and parallel to 1

74

y x

Perpendicular Lines: lines that intersect at _______________ ______________ ; slopes

are _____________________ and _________________________

2) Q: (-6, 2) R: (-1, 8)

S: (-3, 6) T: (-8, 5)

3) through (4, 7) and perpendicular to 2

13

y x

4) through the y-intercept and perpendicular to 3 2 8x y

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Ch 4 Notes Alg 1H 13

p. 239 Check Your Understanding (#1-9)

1. through _________ and parallel to

_______________

2. through _________ and parallel to

_______________

3. through (1, -3) and parallel to

2 1y x

4. through (-2, 2) and parallel to

3 4 x y

5. Sketch: A: (-2, 1) B: (3, -3)

C: (5, 7) D: (-3,4)

6. through (-3, 1) and perpendicular to

12

3y x

7. through (6, -2) and perpendicular to

34

5y x

8. through (2, -2) and perpendicular to

2 5x y

9. through the x-intercept and

perpendicular to 6 6y x

-1 x

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