3.4, 3.5, 3.6, 3.7 TCAP Week 2- Slope

Do Now – (9/3), (√676), ((√13) 2 ) Please pick up your guided notes, get our your SPI Tracker, and respond to the following SILENTLY & INDEPENDENTLY: 1. Which ordered pair is the solution to the following linear system of equations? y – 2x = 3&y = -x - 3 a. (2, 1) b. (-2, 1) c. (2, -1) d. (-2, -1) 2. If the graphs of the equations of a linear system have the same slope, then the linear system has no solution. a. True b. False

Weekly Agenda Monday - Linear vs. nonlinear and slope and y- intercept from equations. Tuesday – Slope from a table, graph, or points. Wednesday – Equations from graphs. Thursday – Quiz Friday – No school!

Today’s Agenda Do Now – 10 Tracking/Review Quiz – 10 INM – 5 BINGO - 20

Today’s Objective SWBAT identify an equation as linear or nonlinear and determine the slope and y-intercept given an equation.  Homework - Worksheet

Linear vs. Nonlinear When graphed, equations can be linear or nonlinear.  Linear Equations  Make a line when graphed.  Indicated by an exponent of 1 on any variable in the equation.  Nonlinear Equations  Make a curve when graphed.  Indicated by an exponent other than 1 on any variable in the equation.

Linear vs. Nonlinear Game Each you of have a card on your desk that says ‘Linear’ on one side and ‘Nonlinear on the other side. Questions will appear on the board and you will have 5 seconds to determine the equation is linear or nonlinear. When directed, please raise the corresponding side in the air.

Linear vs. Nonlinear y = 4x y = x 2 – x +2 y = y = 5 2x + 3y = 10 y = 7x 2 xy = -13 y = -3x – 5 y = 0.75 y = 10x + x2 y = ½x + 2 y = |3x| + 7 k(x) = |x + 6|

Slope-Intercept Form A form of an equation used to identify the slope and y- intercept of a line.  M = slope  B = y-intercept  X = the x coordinate of an ordered pair found on the line  Y = the y coordinate of an ordered pair found on the line  Think subbing a value in to find the other variable (systems of equations) The slope and y-intercept of a line can not be determined if the equation is in standard form (ax + by = c) – YOU MUST CONVERT IT! y = mx + b

Slope-Intercept Form Watch as I walk through this one. Example 1: Determine the slope and y-intercept of the following equation:  ½x = 6y + 12

Slope-Intercept Form Work on this one with your partner. Example 2: Determine the slope and y-intercept of the following equation:  10 = 4y + 13x

Slope-Intercept Form Work on this one with your partner. Example 3: Determine the slope and y-intercept of the following equation:  -5x + 22 = -¼ y

BINGO! Each of you will be given a BINGO card. You will quickly write in any of the answers on the next slide anywhere on your BINGO card. The problems will come up on the board and you will have a minute to answer each problem. You will then see if the answer you determined is on your BINGO card. The first person to get a BINGO wins a prize (Your card will be checked by me to make sure you got answers to the correct problems.)

BINGO ANSWERS /5 -4 -½ / /5 2 -¼ -1/90 1/3 -2/ /7 3 -½ /2 -¼ 5/4 63/ /8 -13/7 43/ ¾ ½ -4 -1/8 5/2 -1/32 2 5/3 3 -1/6 13/8 -27 Fill in your BINGO sheet randomly with these answers

Question 1 Determine the slope of the following equation:  6x + 2y = 4

Question 2 Determine the y-intercept of the following equation:  16=8x + 4y

Question 3 Determine the slope of the following equation:  3x = -5y + 15

Question 4 Determine the y-intercept of the following equation:  – 5x = 20 – 4y

Question 5 Determine the slope of the following equation:  5/7y = 9 – 6x

Question 6 Determine the y-intercept of the following equation:  3y - 2x = -12

Question 7 Determine the slope of the following equation:  5 = ½x + 2/3y

Question 8 Determine the y-intercept of the following equation:  8y = 16 – 2x

Question 9 Determine the slope of the following equation:  2x = 5 – 3y

Question 10 Determine the slope of the following equation:  3y = 21 – 6x

Question 11 Determine the y-intercept of the following equation:  8 = -10x + 4y

Question 12 Determine the slope of the following equation:  10 y = 30 – 90x

Question 13 Determine the y-intercept of the following equation:  ¼x = 4 – ½y

Question 14 Determine the slope of the following equation:  -3y = 6x + 12

Question 15 Determine the y-intercept of the following equation:  -18 = 72y = -9x

Question 16 Determine the slope of the following equation:  11 = 22x – 66y

Question 17 Determine the y-intercept of the following equation:  -4y = x

Question 18 Determine the slope of the following equation:  21x = 49 = 7y

Question 19 Determine the y-intercept of the following equation:  ½y = -1/5x +10

Question 20 Determine the slope of the following equation:  7x = -8y + 13

Question 21 Determine the y-intercept of the following equation:  5 = 2y + 9x

Question 22 Determine the slope of the following equation:  7y = -13x -16

Question 23 Determine the y-intercept of the following equation:  14y = 6x +20

Question 24 Determine the slope of the following equation:  -½ y = -14x + 15

Question 25 Determine the y-intercept of the following equation:  1/8x = -24 – 4y

Question 26 Determine the slope of the following equation:  3y = 9x -10

Question 27 Determine the y-intercept of the following equation:  -90y = -15x +45

Question 28 Determine the slope of the following equation:  -9=1/6x + 1/3y

Question 29 Determine the y-intercept of the following equation:  18y + 1/5 = -7x

Question 30 Determine the slope of the following equation:  43x – 52 = 64y

Do Now – (90/30), (52/2), ( ) 1. What is the solution to the following system of equations: 3x + 2y = 6&-x -2y = 2 2. What is the solution for x when f(x) = g(x)? f(X) = 4x + 9 g(x) = 2(x – 3)

Today’s Objective SWBAT determine the slope from points, a table, or a graph.  Homework - Worskheet

Today’s Agenda Do Now – 10 INM – 10 Trashketball - 30

Slope The slope of a line is referred to as many things:  The rate of change of the line  Rise over run  Steepness The slope of the line can be found using the following equation:m = y2 – y1 x2 – x1 The slope can be found given an equation (yesterday), points, a table, or a graph.

Slope Watch as I walk through this one. Example 1: The points (10, -3) and (9, 4) are found on a line. What is the slope of the line?

Slope Watch as I walk through this one. Example 2: The following table gives points that lie on a line together. Determine the slope of the line.

Slope Watch as I walk through this one. Example 3: Determine the slope of the following graph:

Slope Work on this one with your partner. Example 6: What is the slope of a line with the points (18, 9) and (10 – 5)?

Slope Work on this one with your partner. Example 7: Determine the slope of the line given the information in the table.

Slope Work on this one with your partner. Example 8: Determine the slope of the following graph.

Trashketball You are broken up into groups. A problem will come up on the board and you will work together to determine the answer to the problem in 1 minute. You will write your answer on your group whiteboard. When directed, one member of your group will show your answer by raising your board. If your group answered the question correctly, you will earn a point and have a chance to earn another point by making a basket in the trashketball. If your group misses the question, you do not earn a point and do not get a chance to shoot the ball.

Question 1 What is the slope of a line that passes through (4, -5) and (6, -6)?

Question 2 The table shows the coordinates of three points contained in the graph of a line. What is the slope of the line?

Question 3 What is the slope of the line that passes through the points (-4, -5) and (-12, -9) ?

Question 4 What is the slope of the line?

Question 5 What is the slope of the line that passes through the points (7, 12) and (11, 22)?

Question 6 What is the slope of the line that passes through (-5, 7) and (6, -9)?

Question 7 7) The table below shows the coordinates of three points contained in the graph of a line. What is the slope of the line?

Question 8 What is the slope of the line?

Question 9 What is the slope of a line that passes through (-8, 2) and (0, 0)?

Question 10 What is the slope of the line?

Question 11 What is the slope of a line that passes through (5, 2) and (1, 3)?

Question 12 The table shows the coordinates of three points contained in the graph of a line. What is the slope of the line?

Question 13 What is the slope of the line?

Question 14 The table shows the coordinates of three points contained in the graph of a line. What is the slope of the line?

Question 15 The table shows the coordinates of three points contained in the graph of a line. What is the slope of the line?

Question 16 What is the slope of the line?

Question 17 The table shows the coordinates of three points contained in the graph of a line. What is the slope of the line?

Question 18 What is the slope of the line?

Question 19 The table shows the coordinates of three points contained in the graph of a line. What is the slope of the line?

Question 20 What is the slope of the line?

Question 21 What is the slope of the line that passes through the points (6, 14) and (8, 19)?

Question 22 What is the slope of the line?

Question 23 What is the slope of the line that passes through the points (-14, 0) and (4, -8)?

Question 24 The table shows the coordinates of three points contained in the graph of a line. What is the slope of the line?

Question 25 What is the slope of the line?

Do Now – (-5 + 8), (9 x 3), (√169) 1. What is the solution to the following linear system of equations? y =x - 1&x + y = 5 2. Solve for x when f(x) = g(x). f(x) -3x +4 & g(x) = x -6

Today’s Agenda Do Now – 10 Equations & intercepts review – 10 Pass the problem - 30

Today’s Objective SWBAT write an equation given a graph and determine values of the line.  Homework - Worksheet

Lines Things to remember when determining the equation of the line:  If the line goes up from L to R, the slope is positive.  If the line goes down from L to R, the slope is negative.  The y-intercept is the point where the graph passes the y-axis. Things to remember when finding values of a line:  If you are given an x value, find it on the x axis and follow it to the line and determine the corresponding y value.  If you know the equation, sub the value in and solve for the missing variable. Things to remember about the y-intercept:  The ordered pair for the y-intercept is always (o, y-int).

Lines Watch as I walk through this one. Example 1: Determine the equation of the line, the point of the y-intercept, and if x = 1, what is y?

Lines Watch as I walk through this one. Example 2: Determine the equation of the line, the point of the y-intercept, and when x = -3, what is y?

Lines Work on this one with your partner. Example 3: Determine the equation of the line, the point of the y-intercept, and when x = -3, what is y?

Lines Work on this one with your partner. Example 4: Determine the equation of the line, the point of the y-intercept, and when x = -7, what is y?

Pass the Problem There are cards that will be passed around the room. It is your job to make an equation for each of the cards. Afterward, we will grade your cards to see how you did!

Do Now – (18/6), (14 x 2), (18 – 3) Turn in last night’s homework. Clear off your desk of everything except a pencil, your calculator and a piece of blank paper. Wait silently to begin the quiz! The longer it takes you to do this, the less time you will have for you quiz!