# 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.

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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____

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

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

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

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

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

Linear Part II SLOPE Name ____________ Class _________ 19 21 20 18 22
Change to y=mx+b form 20 18 22

_____________________________
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 \$______

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

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!!!!!!!!!

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=________________

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

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

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

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

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

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?___________

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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