Lesson 11 the Cartesian Coordinate System

BLUE 1

Blue Vocabulary

Definition Example

Abscissa

Cartesian Coordinate System Coincide

Coordinate

Dependent Variable

Domain

Function

Independent Variable

Intersecting

Ordinate

Origin

Parallel Lines

Perpendicular Lines

Quadrant

Algebra One: Unit Two ~ Slope desotocountyschools.org Maggie Dennis & Karen Hatch BLUE 2

Relation

Undefined x-axis x-coordinate y-axis y-coordinate

Lesson 6 The Cartesian Coordinate System Notes

y 10 Label important parts of the Cartesian Coordinate

-10 10 x

Example One y 10

Can you plot 3 points in the third quadrant whose ordinate is -2?

-10 10 x

Lesson 6 The Cartesian Coordinate System Notes

y 10 Example Two

Can you plot 3 points in the secondfirst quadrant whose ordinate is is two more than the abscissa?

-10 10 x

Example Three y The ordered 10 pair (-5, -2) 4 satisfies the y = x + 2 relationship 5 between x and y in the linear equation -10 10 Find three x more ordered pairs that satisfy this equation and graph the -10 ordered pairs. Lesson 6

The Cartesian Coordinate System

DOK 1 On a Cartesian coordinate plane do the following: 1. Plot 3 points in Quadrant III 2. Plot 3 points in Quadrant IV whose x-coordinate whose y-coordinate (abscissa) is -5. (ordinate) is -2. What are the coordinates What are the coordinates of of your points?y your points?y 5 5

-5 5 x -5 5 x

3. On the Cartesian coordinate plane plot the following points: (10,25), (0,5), (-10,-15), (8,21), and (-6,-7). ***You cannot count by ones.*** y 10

-10 10 x

Lesson 6 The Cartesian Coordinate System

Use the coordinate plane below to answer the following:

y 4. What is the ordered pair of A? 5 5. What is the abscissa of B? A C 6. What is the ordinate of C?

7. What is the ordered pair of D? -5 5 x D B 8. Which points have the same abscissa?

-5 9. Which points have the same ordinate?

DOK 2 10. The ordered pair (12,7) satisfies the relationship between x and y in the 2 linear equation y  x 1. Find three more ordered pairs that satisfy this 3 equation and graph the ordered pairs. y 10

-10 10 x Lesson 6

Algebra One: Unit Two ~ Slope desotocountyschools.org Maggie Dennis & Karen Hatch -10 BLUE 7

11. The ordered pair (5,11) satisfies the relationship between x and y in the linear equation y  3x  4 . Find three more ordered pairs that satisfy this equation and graph the ordered pairs. y 10

-10 10 x

12. The ordered pair (9,8) satisfies the relationship between x and y in the 5 linear equation y  x  3. Find three y 9 10 more ordered pairs that satisfy this equation and graph the ordered pairs.

-10 10 x

Lesson 6 -10

Problems #13 – 14, these graphs show relationships between the time and distance traveled: 13. About how far did Jane walk in 3 hours? y . . 40 Distance miles 35

1 2 3 4 5 x Time hours

14. How far did Eric ride his bike in four hours? . y 125 Distance miles 100

1 2 3 4 5 x Time hours Lesson 7 Functions Notes

Example One

-10 10 x {(0,3), (3,0), (1,3)} Is this a function?

How do you know? -10

Example Two y 10 {(0,3), (1,5), (1,3)} Is this a function?

How do you know? -10 10 x

y 10 Example Three {(0,1), (1,4), (4,1), (5,6)} Is this a function? -10 10 x

How do you know? -10

Lesson 7 Functions Notes

Example Four {(-2,4), (1,7), (0, 7), (9,-4)} D: R:

Example Five g(x) = 4x, what is g(2)?

Example Six h(x) = 1/2x – 3, what is h(0)?

Example Seven f(x) = 2x , what is f(4)?

Example Eight f(x) = x3 , what is f(5)?

Example Nine If k(x) = 3x – 2 and its domain is {4,0,1}, what is the range?

Example Ten If k(x) = 3x – 2 and its range is {4,0,1}, what is the domian?

Lesson 7

Functions

DOK 1 1. Which of the following sets represent functions?

F = {(0,1), (0,2), (0,3), (0,4)} G = {(2,1), (3,1), (4,1), (4,1)} H = {(-1,2), (0,4), (2,-1), (4,0)}

2. Which of the following is NOT a function? Explain why it is not. A) y2 = x B) y = x2 + 2

C) y = 2x D) y = 1 – 2x

3. Given the function g(x) = 2x and the DOMAIN {0, 2, 4}, what is the RANGE?

4. Given the function g(x) = 2x and the RANGE {0, 2, 4}, what is the DOMAIN?

Lesson 7

Functions

5. Which graph does NOT represent a function? Explain why it is not.

6. If k(x) = x3 find k(3). 7. If h(x) = 2x + 4 find h(5).

8. The population of a certain bacteria can be approximated using the exponential function p(t) = 22t –t. What is the approximate population of the bacteria after 2 hours?

Lesson 7 Functions

9. The number of students who paid for a cafeteria lunch each day during a one week period was recorded in the bar graph below. What is the DOMAIN of the function?

250 200 150 100 50

M Tu W Th Fr

10. A commercial printer uses the following function to calculate customer cost for p, the number of pieces printed. f(p) = 75 + 0.02p What would be the customer cost for 2000 pieces printed?

Lesson 8 Slope Notes Slope-

y Example One 10 Find the slope of the line that contains the points (-3, 2) and (4, 4).

Algebraically: -10 10 x

Example Two

Find the slope of the line that contains the -10 10 x points (5, -2) and (5, 4).

Algebraically:

Lesson 8 Slope Notes

y 10 Example Three Draw a red line with a positive slope. Draw a blue line with a negative slope. -10 10 x Draw a green line that has an undefined slope. Draw a purple line that has a slope of 0. -10 y Example Four 10

Complete on white board

-10 10 x

-10 10 x Example Five

Algebra One: Unit Two ~ Slope desotocountyschools.org Maggie Dennis & Karen Hatch

-10 BLUE 16

Complete on white board

Lesson 8 Slope DOK 1 1. On the same coordinate plane, do the following: 3 a) Draw a line with slope and label it a. 4 b) Draw a line that is not as steep as line a and label it b.

c) What is the slope of line b? 3 d) Draw a line with slope  and label it d. 4 e) Which line is steeper: line b or line d?

f) Which of the three lines is the steepest? y 10

-10 10 x

Determine the slope for the lines containing the following points: 2. (6, -2) and (2, 2) 3. (-3, -3) and (7, 3)

4. (-6, 2) and (2, 2) 5. (3, -3) and (3,7)

Lesson 8 Slope

y 6. Draw a line that has each of the following 10 described slopes: Positive Undefined Negative Zero

-10 10 x

-10 7. What is the slope of this line? y 5

-5 5 x

8. A loading ramp extends a horizontal distance of 6 feet from a loading dock that is 4 feet high. What is the slope of the ramp?

6 ft Lesson 8 Slope

9. Two rectangular structures are represented by the graph below. Find the slope of the guy wire between the structures represented by the line segment AB. A

10. When Geri first began to lift weights, she could only bench press 20 pounds. After one week, she could bench press 27 pounds. At the end of three weeks, she could bench press 41 pounds. What was her average rate of increase in pounds per week?

11. Jermaine preheats the oven before baking cookies. He notes the temperature at two different time intervals and records them in the data table below. If the temperature increase is constant, what is the rate of change?

Minutes (x) Temp °F (y) 2 225 5 450 Lesson 8 Slope

12. A drywall finisher makes $100 for an 8-hour shift. Which line on the graph below BEST represents total pay, y, for x hours?

y D 100 C

P 80 A Y 60 B 40

1 2 3 4 5 6 7 8 x Hours

13. In order to move a sofa, Mary wants to place a piece of board over her staircase to make a ramp. She knows that the depth of the staircase is 18 feet and the height is 12 feet. Draw a diagram to represent her staircase and determine the slope of the ramp she needs to build.

Lesson 9 Parallel and Perpendicular Lines Notes

Parallel Lines

Are y = 2x - 3 and y = -2x - 3 parallel? Is y = -2x parallel to either of these?

-10 10 x

Lesson 9 Parallel and Perpendicular Lines Notes

Perpendicular Lines

-10 10 x Draw two lines that are perpendicular to one another and go through the point (2, 3).

Lesson 9 Parallel and Perpendicular Lines

DOK 1 1. What is the relationship between the slopes of two lines that are parallel?

2. What is the relationship between the slopes of two lines that are perpendicular?

3. Line p is defined by the equation y = -2x + 1. Which of the following lines is PARALLEL to line p? 1 1 A) y =  x + 1 B) y = x + 1 C) y = 2x -2 D) y = -2x – 1 2 2

4. Line p is defined by the equation y = -2x + 1. Which of the following lines is PERPENDICULAR to line p? 1 1 A) y =  x + 1 B) y = x + 1 C) y = 2x -2 D) y = -2x – 1 2 2

5. What is the slope of y = 7x + 5?

6. What would the slope be of a line perpendicular to y = 7x + 5?

2 7. What is the slope of y = x -11? 3

2 8. What would the slope be of a line perpendicular to y = x -11? 3 Lesson 9 Parallel and Perpendicular Lines

The graph below shows several lines. Each line on the graph will match a PARALLEL line in the list on the left. Match the equations of the lines given on the left to a PARALLEL line on the graph.

(List the slopes of the equations and the lines!) y m = ____; E 10 C m = ______9. y = -3x -2 m = ____ 1 ___ 10. y = x – 1 2 D m = ____

m = ____ -10 10 x ___ 11. y = 3 m = ____ 1 B ___ 12. y =  x + 5 5 m = ____ A -10-10 m = ____ m = ______13. y = x + 2 m = ____

Algebra One: Unit Two ~ Slope desotocountyschools.org Maggie Dennis & Karen Hatch