LINEAR Y=MX + B Part I• A graph is not a function unless all

the ____ values are different. It must pass the __________ Line Test.

• 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!!!!!!

Name_________________ Period____

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Domain Range

• Domain = ____ values• Range = ____ values• A filled in dot means?• An open dot means?• How do you write the domain and

range of discrete graphs?

Coordinate Points

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

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!!!!!!

Here you know x

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Where is x > to 5?

Where is y < -1

Plot (3,4) (-2,3) ( 4, -2) (0,0) (0,6) and (5,0)

Hint!!! Connect the dots and draw diagonals

Plot the points!!!!Connect the dots!!!Which makes a triangle with a 90 degree angle in it??????

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(-3,2)

X<-15 y < -3

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X intercept = ( , ) y intercept = ( , ) 12 13

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More difficult!!!!!!!!!

The graph has corners at ________,_____, _____, ______To be similar, the new figure must be in proportionThe 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.

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Is the slope positive or negative?___That eliminates ____ and ____What is the slope? _____

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More difficult!!!!!!!!!

The graph has corners at ________,_____, _____, ______To be similar, the new figure must be in proportionThe 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.

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Is the slope positive or negative?___That eliminates ____ and ____What is the slope? _____

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SLOPESLOPE

Change to y=mx+b form

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• Linear Part II• Name• ____________• Class• _________

Find (4,-3) on each and eliminate __ and __

Explain why the table of values above cannot be a linear function______________________________________

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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Some Common Sense

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.

Using the slope formula

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.

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…Plug in 3 for x and 4 for y and

see which works

M= ___ - ____ ____ - _____

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Watch out for the y intercept!!!!

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!!!!!!!!!

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.

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Read Carefully!!!!!!!! Are you using thousands of hundred thousands?

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

A = ______________B =_______________C=________________D=________________

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Make sure you distribute first

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?_______

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Solve 104 = 9/5 C +32

Rate of Change = slopeWrite = y = -7 in slope intercept formY = ___x + ____Is the -7 slope or the YI?______What is the missing number next to the x ?

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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 ? ( , )

• Make an x,y table• X Y• 0 Or just plug in each answer (the • 0 store program can help

Suggestions: Graph it on graph paper using the intercepts. Or Plug the intercepts in the answers, or Graph on calculator and use the tables

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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 + 4 and 3x = y + 4 Why?• __________________________________

• 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) • _______________________________

• 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?)_________

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What is the slope of a line perpendicular toA. y = 3/4x -2 ______ D. y = 2x +3 _______B. y= 8/3 x _______ E. y = 6x +5 _______C. y = ¼ x – 5 _______ 49

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DIFFERENCE!!!!!!!!!

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• 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?

___________

Must have the same slope.

Must have a y intercept of 8.

This is when –a/b and c/b comes in handy

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Midpoint • The midpoint formula is on the formula chart.

( ½ , -2) = ( x1 + 6) , (y1 + 1)

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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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