3.4, 3.5, 3.6, 3.7 tcap week 2- slope. do now – (9/3), (√676), ((√13) 2 ) please pick up your...
TRANSCRIPT
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 linearsystem of equations?
y – 2x = 3 & y = -x - 3a. (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. Trueb. 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 – QuizFriday – No school!
Today’s Agenda
Do Now – 10Tracking/Review Quiz – 10INM – 5BINGO - 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 = x2 – x +2 y = y = 5 2x + 3y = 10 y = 7x2
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
-3-2-42/5-4-½428-65/2-9
5-3/52-¼-1/901/3-2/382010/7
3-½ -4715/2-¼5/463/52-3
-7/8-13/743/64-2-¾ 7-23-½-4
-1/85/2-1/322
5/33-1/613/8-27
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 = -8 + 16x
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), (-60 + 73)
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 – 10INM – 10Trashketball - 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.
x y
-1 8
2 3
5 -2
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.x y
-30 2
-20 4
10 6
0 8
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
x y
-1 2
0 4
1 6
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?
x y
10 0
-4 -5
-18 10
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?
x y
-6 -8
0 -5
6 -2
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?
x y
-2 -5
0 0
2 5
Question 15
The table shows the coordinates of three points contained in the graph of a line. What is the slope of the line? x y
7 3
9 7
11 11
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?
x y
-1 1
-2 2
-3 3
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?
x y
10 -10
0 2
-10 24
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? x y
-6 -18
-12 -12
-18 -6
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 linearsystem 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 – 10Equations & intercepts review – 10Pass 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!