Lecture 5 sections 2.1-2.2 coordinate plane and graphs-
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Transcript of Lecture 5 sections 2.1-2.2 coordinate plane and graphs-
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
MATH 108
Section 2.1-2.2
Coordinate Plane and Graphs
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
x axis
y axis
origin
Rectangular/ Cartesian Coordinate System/ Plane
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Let's plot the point (6,4)
(-3,-5)
(0,7)Let's plot the point (-6,0)
(6,4)
(-6,0)
Let's plot the point (-3,-5) Let's plot the point (0,7)
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Quadrant I x > 0, y > 0
Quadrant II x < 0, y > 0
Quadrant III x < 0, y < 0
Quadrant IVx > 0, y < 0
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Find the distance d between the points (2, - 4) and ( -1, 3).
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Find the midpoint of the line segment from P1 = (4, -2) to P2 = (2, -5). Plot the points and their midpoint.
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Section 2.2
Graphs of Equations
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Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Find the slope m and y-intercept b of the equation -12x + 3y = 6. Graph the equation.
Find the slope m and y-intercept b of the equation --x + 4y + 5 = 3. Graph the equation.
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DefinitionsAny point where a graph intersects the x-axis has the form (a, 0). The number a is called an x-intercept of the graph. y = 0
Similarly, any point where a graph intersects the y-axis has the form (0, b), and the number b is called a y-intercept of the graph. x = 0
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
PROCEDURE FOR FINDING THE INTERCEPTS OF A GRAPH
Step 1 To find the x-intercepts of an equation, set y = 0 in the equation and solve for x.
Step 2 To find the y-intercepts of an equation, set x = 0 in the equation and solve for y.
14© 2010 Pearson Education, Inc. All rights reserved
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Graph the linear equation 3x + 2y = 6 by finding its intercepts.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Write the standard form of the equation of the circle with radius 4 and center (2, -4).
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2 2Graph the equation: 4 1 9x y
2 2 2(4 1) 3x y
2 2 2h rx y k
Center: 4, 1 Radius: 3
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
2 2For the circle 4 1 9, find the intercepts,
if any, of its graph.
x y
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Change from general form to standard form (by completing the square):
x2 + y2 – 8x + 4y – 5 = 0
x2 + y2 + 2x + 6y – 26 = 0