Unit 2: Linear Functions This chapter will include some review from last year. Mostly, we will be solving equations – lots of equations! 2.1 Multiple Representations of Mathematical Relationships WARNING: This lesson takes The entire class period, and there Really isn’t any time for a quiz!!

Find at least ONE solution for y = -2x + 9x +8 – 5x Write down this problem on your COMMUNICATOR Be prepared to share your work with the class. determine if the graph of this equation is linear or not. Page 24 of your INB The point of this recall question Is to get students thinking about How to generate solutions. Hint: pick 0 to be x. That’s The easiest way to generate One quick solution. Other solutions can be generated By picking other values for x, And then evaluating for y. y -3x = 0

ITEMS of BUSINESS Monday (A-day students) is last day to retake Ch. 1 Test Tuesday (B-day students) is last day to retake Ch. 1 Test Be sure to tell Mrs. Kalt if you want to retake in intervention on Monday (A-day students) or Tuesday (B-day students) And be sure to study well for the retake. It can make a BIG difference! CHAPTER 2 TEST is next Wednesday/Thursday PARENT TEACHER CONFERENCES next Wednesday/Thursday 3:45 – 7:15

Have your homework out on your desk.

People with 100%, try this honors question: Is this a function? Why or why not? Nope. NOT a function. First of all, it fails the vertical line test. A vertical line hits ALL points on that graph. Secondly, You can see that every point on the graph is (3,y). For example (3,0), (3,1), (3,2), (3,3), etc. The x-value 3 goes to infinitely many y-values!

Get into your 4-Square Groups Page of your INB determine if the graph of this equation is linear or not. y -3x = 0 While students are answering The i-can, pass out ipads. No Opening them until I say. Review Ipad rules. Ask students to answer the i-can. By raise of hands, who thinks This is linear? Who thinks it is not linear? Keep your hand up if you know WHY it’s not linear?? Call on Students to tell why they think it Is not linear.

y = 2x + 4 Review with students how To graph solutions of Equations. 1)Generate 3 points 2)Plot points 3)Draw the line Why not just 2 points? Is 3 enough? Shall we keep generating points? Are you sure what direction it’s Heading?? Fill in with dots... Ok, ok, you can just draw a line. Strategy: 1) Generate 3 solutions. 2)Plot the points. 3)Connect the dots.

I wonder if equations are ALWAYS linear... ??? I know what you’re all wondering. Or at least you should be wondering this...

Or maybe Mrs. Kalt is spoon feeding me equations that are easy to digest??? y = x + 1 Is it possible that I have been Spoon-feeding you applesauce Equations? Equations that don’t require any Chewing??? Yes, I’ve been giving you baby Food equations.

y = x 2 Use our same strategy: 1)Generate 3 points 2)Plot points 3)Draw the line Notice that the 3 points Are NOT in a straight Line!! Have students connect the dots And hold them up on their Communicators. Ask them how do you know it Doesn’t go up and down and up And down?? Strategy: 1) Generate 3 solutions. 2)Plot the points. 3)Connect the dots.

y = │ 3x - 1 │ Same strategy here. Discuss what absolute value Means. Again, have students connect Their 3 dots. So if we don’t know where a Graph is headed, what can we do? Should we continue generating Solution points??? Strategy: 1) Generate 3 solutions. 2)Plot the points. 3)Connect the dots.

So how do you know if it’s a straight line? Do you have to generate like a million points to see what it’s going to look like?

or you could use... Yes, you could just sit there And keep generating points. That’s what we used to do in The olden days. Now-a-days you have Awesome tools, like graphing Calculators and apps on ipads. You may now open your ipads.

FIRST Go to desmos website and teach them How to graph each of the parent functions. They will put the parent function equation And matching graph, one on each desk. Then have them sketch the graph of each. SECOND Define names of graphs: Absolute value Linear Quadratic Cubic Have them divvy up the “child” equations Amongst themselves and start graphing Them in desmos. They will sort them out On their desks as they go. Also, they Will write them on their papers. THIRD Do a whole-class sort on the board. FOURTH Have them describe common characteristics. y = │x│ y = x y = x 2 y = x 3 name of graph Describe the common characteristic: List the equations that belong to the parent graph above. Describe the common characteristic: List the equations that belong to the parent graph above. Describe the common characteristic: List the equations that belong to the parent graph above. Describe the common characteristic: List the equations that belong to the parent graph above.

Draw or write something to defend your claim.

Show how the following Equations fit into this format. Y = =3x – 4 Y = 9x Y = -x

Answers: 1.m/9 – y (write division the big-boy way plz) 2.K-10 = h 3.b=2a – 5 (students will write b =5-2a) Ask: what is 5 less than 20? 20-5 compare 4. 2n+8 = y Simplify: Show it fits the format for linear equations:

y 2 = x Every x goes to ONE y. Equations with variables. y=x 2 y=2x+1

Ladies first!

Don’t forget, when graphing:

How do I know which is DEPENDENT And which is INDEPENDENT? Then ask yourself: Does ___________ depend on __________ or does ___________ depend on ___________? $total spent# of cans $total spent# of cans First determine the unknowns. ___________ & ___________ $total spent# of cans The TOTAL DEPENDS... # OF CANS is INDEPENDENT 17.

SHOW YOUR WORK Worksheet 2.4 Linear or Not?