W ELCOME TO C HAPTER 4!

PSAE P RACTICE 1. You are the new maintenance person for the local school and need to calculate how much wax will be required for the cafeteria floor based on its square footage. The cafeteria is 120 feet by 45 feet. What is the square footage you should use to figure the amount of wax needed for the cafeteria floor? a) 165 ft 2 b) 100 ft 2 c) 1000 ft 2 d) 5400 ft 2 e) 6000 ft 2 2. You must set up tables for a wedding reception in the restaurant where you work. There will be 24 individuals and 40 couples attending. Each table seats 8 persons. How many tables should you set up? a) 3 b) 5 c) 10 d) 12 e) 13

4.1 – C OORDINATES O BJECTIVE : T O PLOT POINTS AND NAME POINTS IN THE COORDINATE PLANE. A is formed by two real number lines that intersect at the origin. (x-axis and y-axis) An is a point in the coordinate plane represented by real numbers. The x-coordinate is the first number. The y-coordinate is the second number. Ex. (3,6) (x, y)  (right or left, up or down)

T HINK OF COORDINATE POINTS AS AN … (x, y)  You must move (horizontally) into the elevator before you can go up or down.

C OORDINATE PLANE ( X, Y ) x- axis y-axis Origin (0,0) Quadrant I (+, +) Quadrant II (-, +) Quadrant III (-, -) Quadrant IV (+, -)

P LOTTING POINTS Then 4 up (positive) make a point Plot these points: 1.(-2, -4) 2.(0, 3) 3.(-1,0) 4.(6,-2) 5.(-4, 5) To plot a point: (3,4) Start at (0,0) Move 3 to the right (positive)

P RACTICE Name the following points and give the quadrant or axis where they lie. A: B: C: D: A B C D

B C D E F Identify the ordered pairs on the coordinate plane. Name the quadrant it is in or the axis it is on. A  ________ Quad _____ B  ________ Quad _____ C  ________ Quad _____ D  ________ Quad _____ E  _________ Quad _____ F  ________ Quad _____ A N AMING P OINTS

The Coordinate Plane Steps to Make a Scatter Plot: 1. Determine what will be x and y. I. x – is in charge, it changes automatically II. y – depends on x, is not automatic 2. Determine units of each axis and label. I. Find range of variable II. Divide range by number of squares III. Always round up to “nice” unit 3. Plot points.

Make a Scatter Plot Example The age (in years) of seven used cars and the price (in thousands of dollars) paid for the cars are recorded in the table. Make a scatter plot and explain what it indicates age of car price in $1,000 Age Price How much would a 2-year old car cost?

Make a Scatter Plot Example The amount (in millions of dollars) spend in the United States on snowmobiles is shown in the table. Make a scatter plot and explain what it indicates. Year Spent

L ESSON 4.1 DHQ NONE TODAY Tonight’s Homework Assignment: Coordinate WORKSHEET

W ARM -U P Solve each equation for y. 1) 2x + y = 102) 6x – 3y = -3 Find the value of y when x = -3. 3) y = x – 7 4) y = -5x + 1

4.2 – G RAPHING L INEAR E QUATIONS OBJECTIVES Graph a using a table. Graph and lines. linear equation horizontalvertical Note (1) All the Equations in Chap 4 refer 2 variable Linear Equations. (2) The graph of each linear equation is a LINE.

S OLUTION OF AN E QUATION It is an ordered pair (x, y) that makes an equation true. Example: x + 3y = 6 Is (-3, 3) a solution?

I S (-3, 3) THE ONLY SOLUTION ? x + 3y = 6 In pairs, try to come up with other solutions to the equation! Try to come up with at least 2 more solutions.

x + 3y = 6 SOLUTIONS OF THE EQUATION Solutions: What would it look like if we plotted the solutions of the equation on a coordinate plane?

S OLUTIONS TO A L INEAR E QUATION All the that lie on the line are the solutions to the ! points equation How many solutions did we have in our previous example?

H OW TO C HECK IF A P OINT IS A SOLUTION Method 1: Using a Graph Check to see if the point is on the line. Is (3, 1) a solution of the equation 2x – y = 5? Is (0, -4) a solution of the equation 2x – y = 5? Is (5, 5) a solution of the equation 2x – y = 5?

H OW TO C HECK IF A P OINT IS A SOLUTION Method 2: Checking algebraically Plug the point into the equation and see if it is true. Is (3, 1) a solution of the equation 2x – y = 5? Is (0, -4) a solution of the equation 2x – y = 5? Is (5, 5) a solution of the equation 2x – y = 5?

BREAK TIME Use this time to relax, stretch out, talk to a neighbor, or try the following rebus puzzles.

U SING A TABLE TO GRAPH AN EQUATION Steps: 1. Rewrite the equation so that it says “y = …” – (called function form) 2. Make a table and choose values for x. 3. Plot the points on a coordinate plane and graph with a straight line.

U SE A TABLE TO GRAPH THE FOLLOWING EQUATION y + 1 = 2x Step 1: Rewrite the equation so that it says “y = …” Step 2: Make a table and choose values for x. xy

U SE A TABLE TO GRAPH THE FOLLOWING EQUATION y + 1 = 2x Step 3: Plot the points on a coordinate plane and graph with a straight line. xy

P AIRS P RACTICE Graph y + 2 = 3x. xy

P AIRS P RACTICE Graph y + 3 = x. xy

G RAPHING H ORIZONTAL AND V ERTICAL L INES Horizontal = left to right Vertical = up and down x = any number y = any number MEMORIZE THIS! vertical line horizontal line

H ORIZONTAL L INES

G RAPH THE FOLLOWING E QUATION y = 5 Horizontal line where every y- coordinate on the line is 5.

G RAPH THE FOLLOWING E QUATION y = -1

V ERTICAL L INES

G RAPH THE FOLLOWING E QUATION x = -3 Vertical line where every x-coordinate on the line is -3.

G RAPH THE FOLLOWING E QUATION x = 5

L ESSON 4.2 DHQ Decide whether the given ordered pair is a solution of 2x – 3y = 8. a.(-2, -4)b. (7, -2) Rewrite 4x – 2y = 18 in function form. Tonight’s Homework Assignment: Page/s: #’s 15-20, 30-32, 36-37, 60

4.3 - Q UICK G RAPHS U SING I NTERCEPTS Objectives: Find the intercepts of a graph of a linear equation.

H OW MANY POINTS DOES IT TAKE TO DETERMINE A LINE ? We need at least two points to determine a line.

I NTERCEPTS x-intercept – the point where a line or curve crosses the x-axis. This is always written as (x, 0). y-intercept – the point where a line or curve crosses the y-axis. This is always written as (0, y).

I NTERCEPTS x-intercept? y-intercept? (0, 3) y = 3 (2, 0) x = 2

W HAT IF WE ARE NOT GIVEN A GRAPH ? H OW DO WE DETERMINE THE X AND Y - INTERCEPTS ?

W E CAN FIND THE … x-intercept by setting y = 0 y-intercept by setting x = 0

F IND THE X - INTERCEPT AND Y - INTERCEPT OF THE GRAPH OF THE FOLLOWING EQUATION. To find the x-intercept, set y = 0 and solve for x. To find the y-intercept, set x = 0 and solve for y. 2x + 3y = 6

F IND THE X - INTERCEPT AND Y - INTERCEPT. T HEN GRAPH THE LINE x – y = 4

F IND THE X - INTERCEPT AND Y - INTERCEPT. T HEN GRAPH THE LINE y – 2x = 3

B REAK T IME Use this time to relax, stretch out, talk to a neighbor, or try the following rebus puzzles.

F IND THE X - INTERCEPT AND Y - INTERCEPT. T HEN GRAPH THE LINE y = 2x + 4

G RAPH AND WRITE THE EQUATION OF THE HORIZONTAL LINE PASSING THROUGH (3, -4) AND (-6, -4)

G RAPH AND WRITE THE EQUATION OF THE VERTICAL LINE PASSING THROUGH (3, 2) AND (3, -5)

R ECAP : 1. The x-intercept and y-intercept are the points at which a line or curve cross the x and y-axis, respectively. 2. To find the x-intercept, set y = To find the y-intercept, set x = We can graph a line by connecting the two intercepts.

L ESSON 4.3 DHQ 1.Give the x- and y- intercepts of the graph of 2x – y = Graph 2x – 3y = 6. Label the points where the line crosses the axes. Tonight’s Homework Assignment: Page/s: #’s 35-37, 44-49, QUIZ Friday

4.4 – S LOPE OF A L INE

Have you ever… walked up a ramp? skied down a hill? jumped to dunk a ball? What are some other examples?

m = rise run vertical change horizontal change

What is the slope?

Check:

m = rise run What is the rise of any horizontal line?

m = rise run What is the run of any horizontal line? Check: Try to divide any number by zero!

Positive Slope = Going up the chair lift. The height increases. Negative Slope = Going down the hill. The height decreases. Horizontal Slope = The height on the ground is zero and stays the same as you move. Undefined Slope = Most skiers that look at a hill that drops would say this is impossible!

F IND THE SLOPE PASSING THROUGH THE POINTS ! Check:

F IND THE SLOPE PASSING THROUGH THE POINTS ! Check:

F IND THE SLOPE PASSING THROUGH THE POINTS ! Check:

F IND THE VALUE OF Y.

L ESSON 4.4 DHQ Tonight’s Homework Assignment: Page/s: #’s 23-28, 35-36, *38 1.Find the slope of the line. Use formula to find the slope. a.(-2, 2), (0, 4) b.(1, 1), (4, 2) 2. Find the slope of the line.

L ESSON 4.6 W ARM - UP Rewrite 4x – 2y = 18 in function form.

Write and graph linear equations in slope-intercept form!

Where a line crosses the y-axis. Organization Check: We can now graph an equation in three different ways: 1.Using an x, y table 2.Using x-intercepts, y- intercepts 3.Slope-intercept form

W RITE THE EQUATION IN SLOPE - INTERCEPT FORM, THEN GRAPH. Steps: 1.Set equation to y= 2.Identify the y-intercept (b) and plot it on y axis 3.Identify the slope (m) and plot 1-2 additional points beginning at the y-int (b) 4.Draw your line, with arrows!

Write the equation in slope- intercept form, then graph.

W RITE THE EQUATION IN SLOPE - INTERCEPT FORM, THEN GRAPH.

Use this time to get up, stretch out, relax, talk to a neighbor, or try the following rebus puzzles…

Two different lines in the same plane are _______ if they do not intersect.

Lines are parallel if they have the same ______.

y = 2x + 3 y = 3 + 2x

y = -2x + 3 y = 3 + 2x

4x + 2y = 8 y = -2x + 2

L ESSON 4.6 DHQ 1.Write x + y + 3 = 0 in slope-intercept form. Then graph the equation. Tonight’s Homework Assignment: DUE TOMORROW! Page/s: #’s 13-18, 29-31, 34-36, QUIZ TOMORROW – L 4.4/4.6 – STUDY!

1. What is the slope of the line 5 y = -3 x +10 ? a. -3b. c. d. 2e What is the lowest value of x that satisfies the equation x 2 – 7 x + 6 = 6 ? a. -3b. -6c. 0d. 6e. 1

Section 4.8

Identify when a relation is a function. He knows how to do that, and soon you will too!

What is a function? A function is a rule that establishes a relationship with an input and an output. input output

For every input, there is exactly _____ output! one

Input0113 Output3132

Input0113 Output3112

Input0123 Output3456

There are rules that associate more than one output for each input. But, we can’t call it a function anymore. We call it a…

Any set of ordered pairs! It doesn’t matter how many different outputs an input has!

Yes No

Complete #1-3 on your in-class practice Read the instructions carefully If you have a question, raise your hand

Vertical Line Test – a relation is a function, if NO vertical line passes through two or more points!

Functio n Relation – Not a function

Complete #4-6 on your in-class practice Read the instructions carefully If you have a question, raise your hand

f(x) = 2x – 3 when x = -2, 0, and 3 Steps: 1. Write the original function. 2. Substitute -2 for x. 3. Simplify.

g(x) = -5x + 3 when x = -3, 0, and 1

Complete #7-9 on your in-class practice Read the instructions carefully If you have a question, raise your hand

Graph f(x) = -2x + 3 Steps for using slope-intercept form: 1. Rewrite the function as “y = …” 2. Find y-intercept and slope. 3. Graph and connect.

Graph f(x) = x + 4 Steps for using intercepts: 1.Find the x-intercept by setting y = 0. 2.Find the y-intercept by setting x = 0. 3.Plot the intercepts on the coordinate plane and graph the line.

Next to graphs done by slope-intercept (2 done by this method) Next to graphs done by using x and y-intercepts (1 done by this method)

pgs #16-17, 20-21, Chapter 4 Test Next Week!