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LINEAR Y=MX + B Part I A graph is not a function unless all the ____ values are different. It must pass the __________ Line Test. 1 2 y depends on x. left depends on right. h = 3q +4 h depends on d h=independent q = dependent Numbers are not dependent…only variables!!!!!! 3 Name_________________ Period____

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**Domain Range Coordinate Points 6 5 4 Here you know x 7**

Any time you see a coordinate point, there is an x and a y. In the above you need to find “X”. You know y = -4 so you solve for x. Label the Quadrants!!!!!! 4 Ordered pairs are points on a graph. They are always written in the form (X, Y) (X comes before Y in the alphabet) You can graph ordered pairs on a graph. Ordered pairs are also called “coordinate points” on a graph. Problems on TAKS are often written as ordered pair problems Domain = ____ values Range = ____ values A filled in dot means? An open dot means? How do you write the domain and range of discrete graphs? Here you know x 7

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**Which makes a triangle with a 90 degree angle in it??????**

11 10 Plot (3,4) (-2,3) ( 4, -2) (0,0) (0,6) and (5,0) 8 9 Plot the points!!!! Connect the dots!!! Which makes a triangle with a 90 degree angle in it?????? Where is x > to 5? Where is y < -1 Hint!!! Connect the dots and draw diagonals

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**X intercept = ( , ) y intercept = ( , ) 13**

X<-15 y < -3 12 X intercept = ( , ) y intercept = ( , ) 13 (-3,2) 14

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**Is the slope positive or negative?___**

More difficult!!!!!!!!! 15 16 Is the slope positive or negative?___ That eliminates ____ and ____ What is the slope? _____ The graph has corners at ________,_____, _____, ______ To be similar, the new figure must be in proportion The graph is 4 units high and 2 units wide. Check it. Draw the other 4 figures on the graph. The correct one must have the same multiples of 4 and 2, such as 2 and 1 or 8 and 4. 17

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**Is the slope positive or negative?___**

More difficult!!!!!!!!! 15 16 Is the slope positive or negative?___ That eliminates ____ and ____ What is the slope? _____ The graph has corners at ________,_____, _____, ______ To be similar, the new figure must be in proportion The graph is 4 units high and 2 units wide. Check it. Draw the other 4 figures on the graph. The correct one must have the same multiples of 4 and 2, such as 2 and 1 or 8 and 4. 17

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**Linear Part II SLOPE Name ____________ Class _________ 19 21 20 18 22**

Change to y=mx+b form 20 18 22

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**_____________________________**

23 24 Explain why the table of values above cannot be a linear function_________ _____________________________ Find (4,-3) on each and eliminate __ and __ 25 If 80 is the total and x is the $35 backpacks, how can we write the number of $50 backpacks in terms of 80 and $35? ( ) And we will multiply that by $______

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**Using the slope formula**

Some Common Sense Using the slope formula M= ___ - ____ ____ - _____ 27 Your equation must have a slope that can be determined by these two points as any two points can only be connected by one unique line. So make (7,5) point 1 and (11,9) point 2. (It does not matter, you can make them 2 and 1.) So x2 = ____ and y2 is_____ and x1 is ____ and y1 is ____ Use the formula and find the slope. Slope = ____ But that only narrows it to ____ and ____ Use y = program on these two and see which one passes through both points. 26 The slope formula does not help much here. It gives you a slope of ____ Which does eliminate ___ But you must change GH and I to slope intercept form to get their slopes. Too much work!!!! Y = also requires you to make the changes soooo… Slope is easy here because every answer has the same slope. So this must be a y intercept problem. So, use a straight edge on BOTH graphs and see where they touch the y axis. Be careful as you must be precise. 28 Plug in 3 for x and 4 for y and see which works

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**Watch out for the y intercept!!!!**

30 29 You MUST change from Standard to slope intercept!!!!! Change 6x + 3y = 12 Then change 6x + 3y = 36 What happened to the y intercept? This is when it is good to know the y intercept is C/B First equation c/b =____ 2nd equation C/B = ______ Compare them. A. look at 5000, how much is the earnings?____ B. look at 0 sales, does he still make money?____ C. Look at 1000 (not 10,000), how much commission?________ D. Look at 5000 again. Commission?__________ DON’T GET FOOLED!!!!!!!!!

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**31 32 33 A = ______________ B =_______________ C=________________**

Read Carefully!!!!!!!! Are you using thousands of hundred thousands? 31 32 Graph both on the grid. Is the slope changed at all?___ If a graph passes through the origin, what will the y intercept be?____ Is -3 and increase over 8?______ Did the x intercept get larger?______ Graph on calculator to check 33 A = ______________ B =_______________ C=________________ D=________________

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**This requires you find both the slope and the Y In.**

If you translate it down 2 units what will the new Y In be?____ So, now is the slope 1/3 or 3? _______ 34 36 35 Make sure you distribute first

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**38 37 Solve 104 = 9/5 C +32 39 40 Rate of Change = slope**

Write = y = -7 in slope intercept form Y = ___x + ____ Is the -7 slope or the YI?______ What is the missing number next to the x ? 38 37 Solve 104 = 9/5 C +32 39 40

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**LINEAR Part III Name_____________ Class_________**

Define the word intercept ________________ We have already discussed the fact that the coordinate point of the y intercept of a line that crosses the y axis at 6 must start with a zero (0,6) so what should the x intercept that crossed the x axis at 5 start with ? ( , ) 44 41 Make an x,y table X Y Or just plug in each answer (the store program can help 42 45 Suggestions: Graph it on graph paper using the intercepts. Or Plug the intercepts in the answers, or Graph on calculator and use the tables 43

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**Parallel and Perpendicular Lines**

Parallel Lines have the same slope with different y intercepts. Example y = 3x +4 y = 3x -2 The same line has the same slope and the same y intercept. These lines are parallel. y = 3x and 3x = y + 4 Why? __________________________________ What is the slope of a line perpendicular to A. y = 3/4x -2 ______ D. y = 2x +3 _______ B. y= 8/3 x _______ E. y = 6x +5 _______ C. y = ¼ x – 5 _______ 46 49 50 Perpendicular lines have the negative inverse (reciprocal) slope Y = 2x +4 y =- ½ x -2 What is the equation of a line perpendicular to y= ¼ x -3 that passes through (6,0) _______________________________ 47 Change 3x + 2y = 12 to y=mx+b form. Are the slope the same?____ Is the y intercept the same?____ If they are perpendicular they must have opposite sign slopes…Do they?_______ Are the slopes the negative inverse (reciprocal?)_________ 48

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52 51 DIFFERENCE!!!!!!!!!

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53 Must have the same slope. Must have a y intercept of 8. This is when –a/b and c/b comes in handy 54 55 I wonder if it would help to see if the point (4,7) is on every line ? Use y= to try this. Okay, now what? Change -3x + y =4 to y=mx +b form. Parallel lines must have what slopes?___________

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**The midpoint formula is on the formula chart.**

56 57 ( ½ , -2) = ( x1 + 6) , (y1 + 1) So? Look at the answers. What plus 6 divided by 2 is ½? What plus 1 divided by 2 is -2? _____

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Domain: a set of first elements in a relation (all of the x values). These are also called the independent variable. Range: The second elements in a relation.

Domain: a set of first elements in a relation (all of the x values). These are also called the independent variable. Range: The second elements in a relation.

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