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Math 374 Graphs. Topics Cartesian Plane Methods of Graphing Intercept Slope Scale First Quadrant Inequality Graphs Region.

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Presentation on theme: "Math 374 Graphs. Topics Cartesian Plane Methods of Graphing Intercept Slope Scale First Quadrant Inequality Graphs Region."— Presentation transcript:

1 Math 374 Graphs

2 Topics Cartesian Plane Methods of Graphing Intercept Slope Scale First Quadrant Inequality Graphs Region

3 Cartesian Plane Named after Rene Deo Cartes a french mathematician Also a philosopher I think therefore I am His goal was to create a picture that could show a relationship between two variables. We have one for one variable – the number line.

4 Notes We recall

5 Some Facts We only need two points to draw a straight line The point where a graph crosses or touches the x axis is called the x intercept It is found by substituting y = 0 The point where a graph crosses or touches the y axis is called the y intercept It is found by substituting x = 0

6 Intercept Method Calculate both intercepts. Place on graph and join Example #1: y = 2x – 6 X intercept (y = 0) 0 = 2x – 6 -2x = - 6 x = 3

7 Intercept Method Now find Y intercept Example #1: y = 2x – 6 Y intercept (x = 0) y = 2 (0) – 6 y = -6

8 Finding X and Y Intercept Example #2: 5x – 3y = 15 x int (y = 0) 5x – 3(0) = 15 5x = 15 x = 3 y Int (x = 0) 5(0) – 3y = 15 -3y = 15 y = -5

9 Drawing on Graph Now that you know the x & y intercept, you have two points and now can draw the straight line… do it! Practice plotting with other points…

10 Plotting. C (-4, -4).... B (-4, 2) D (2, -2) (A 3, 1) Q1 (+,+) Q4 (+,-) Q3 (-,-) Q2 (-,+) A (3,1) B (-4,2) C (-4, -4) D (2, -2)

11 Standard Form Method All straight lines have a y intercept and a slant called a slope. If the relationship is in standard form we can write it… y = m x + b Slope Y intercept

12 Y Int Slant Y Int Identifying Slant and Slope

13 Standard Form Recall y = mx + b Dependent Variable (DV) Slope Independent Variable (IV) Y Intercept or Starting Value

14 Relationship of y & b It is easy to see how b is the y intercept; we substitute x = 0 x = 0 y = m(0) + b y = b

15 Rise, Run & Slope Slope Rise Run Rise Run Slope

16 Understanding the Slope If m or the slope is 2 this means a rise of 2 and a run of 1 (2 can be written as 2 ) 1 If m = - 5, this means a rise of -5 and right 1 If m= -2 this means rise of -2 right 3 3

17 Understanding the Slope Consider m = -3 4 What is the rise and what is the run? Suggest to put the negative sign on the top to clarify (rise of -3) Numerator always rise (could go up or down) Denominator always run (right only) Rise Run

18 Consider y = 2x + 3 What is the slope, rise, run and y intercept? We have a slope 2 2 can be written as 2 1 Rise of 2 Run of 1 y intercept of 3 (y = b) Plot on graph paper the following…

19 Ex#1: y=2x+3 0,3 (1,5) Question: Draw this line What is the y intercept? What is the slope What does the slope mean? Where can you plot the y intercept? Up 2, Right 1

20 Example #2 y = -5 x What is the y intercept, slope? Rise and run? Y intercept is 1 Slope is -5/7 Rise is – 5 Run is 7 Plot on graph (put it on graph paper)

21 Example #3 y = x What is the y intercept, slope, rise and run? y intercept = 0 (y int let x = 0) Slope = 1 Rise of 1 Run of 1 Plot on graph

22 Example #4: 3x – 4y = 12 What is the y intercept, slope, rise and run? Must put in standard form -4y = - 3x + 12 y = 3x – 3 4 y intercept = -3 Slope ¾ Rise of 3, run of 4 Plot on graph

23 Graphing with Scale Scale is mostly used to make sure your graph can be seen Consider y = 2x

24 Ex#5 y=2x Ex#5 y=2x (0,100) (300,300) 500 x y You can put 500 along the x axis which means each hash mark is 100 Y intercept? Slope? How will you measure m = 2/3? Note slope is a ratio so scale does not effect it

25 Ex. #5 200x + 300y = y = - 200x Y = -2x Plot it Do #4 on stencil use form C

26 1 st Quadrant There will be times when you will need to put the graph only in the 1 st quadrant The problem only exists when the y intercept is negative In that case, work with the x intercept (sub y = 0)

27 Consider y = 2x – 5 3 Show how the graph intersects in the 1 st quadrant Notice that b is negative. In those cases, work with x int (let y = 0) 0 = 2x – = 2x – 15 -2x = -15 x = 7.5 Stencil: Do #5

28 Inequality Graphs The straight line of the graph divides the plane into two regions One side will be greater than, one side less than

29 The Trick in Standard Form If greater then shade above > If less then shade below < If equal then solid line If not equal then dotted line

30 Ex y > x x y Y intercept? Slope? Step 1: Draw Line m = 1 (up 1, right 1) Dotted Line or solid? Shade above or below?

31 Ex y < x x y Y intercept? Slope? Step 1: Draw Line m = 1 (up 1, right 1) Dotted Line or solid? Shade above or below?

32 Ex 5x - 10y < 30 5 x y y intercept? Slope? Step 1: Put in Standard Form m = 1 (up 1, right 2) Dotted Line or solidline? Shade above or below? -10y < - 5x + 30 y > 1x – 3 2 Do #6 in C

33 Point of Intersection If we have two graphs, we create four regions

34 Consider y > 3x – 5 y < -2x + 5 Consider y > 3x – 5 y < -2x x y Draw lines… one at a time Slope? Hint… with 2 lines, use arrows at first instead of shading m = 3 (3 up, right 1) Dotted Line or solid? Shade above or below? y intercept of 1 st ? 2 nd line… y int? Slope? Dotted / solid? Use arrows Above or Below? Shade where they intersect!

35 Find POI (Point of Intersection), you can also use equations y = 3x – 5 y = -2x + 5 3x – 5 = -2x + 5 5x = 10 x = 2 x = 2 y = 3(x) – 5 y = 3 (2) – 5 y = 1 POI (2, 1) Do 7 in E Finish Study Guide


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