Lecture 5 sections 2.1-2.2 coordinate plane and graphs-
- 1. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. MATH 108 Section 2.1-2.2 Coordinate Plane and Graphs
- 2. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. x axis y axis origin Rectangular/ Cartesian Coordinate System/ Plane
- 3. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. −8−7−6−5−4−3−2−1 1 2 3 4 5 6 7 8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 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)
- 4. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Quadrant I x > 0, y > 0 Quadrant II x < 0, y > 0 Quadrant III x < 0, y < 0 Quadrant IV x > 0, y < 0
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- 6. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the distance d between the points (2, - 4) and ( -1, 3).
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- 9. 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.
- 10. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 2.2 Graphs of Equations
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- 12. 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.
- 13. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 13© 2010 Pearson Education, Inc. All rights reserved Definitions Any 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
- 14. 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
- 15. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Graph the linear equation 3x + 2y = 6 by finding its intercepts.
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- 19. 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).
- 20. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. ( ) ( ) 2 2 Graph the equation: 4 1 9x y− + + = ( ) ( ) 2 2 2 (4 1) 3x y −+ − =− ( ) ( ) 2 2 2 h rx y k+ − =− ( )Center: 4, 1 Radius: 3−
- 21. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. ( ) ( ) 2 2 For the circle 4 1 9, find the intercepts, if any, of its graph. x y− + + =
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- 23. 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