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


x axis

y axis

origin

Rectangular/ Cartesian Coordinate System/ Plane


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)


Quadrant I x > 0, y > 0

Quadrant II x < 0, y > 0

Quadrant III x < 0, y < 0

Quadrant IVx > 0, y < 0


Find the distance d between the points (2, - 4) and ( -1, 3).


Find the midpoint of the line segment from P1 = (4, -2) to P2 = (2, -5). Plot the points and their midpoint.


Section 2.2

Graphs of Equations


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.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.13© 2010 Pearson Education, Inc. All rights reserved

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


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.

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Graph the linear equation 3x + 2y = 6 by finding its intercepts.


Write the standard form of the equation of the circle with radius 4 and center (2, -4).


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


2 2For the circle 4 1 9, find the intercepts,

if any, of its graph.

x y


Change from general form to standard form (by completing the square):

x2 + y2 – 8x + 4y – 5 = 0

x2 + y2 + 2x + 6y – 26 = 0

Lecture 5 sections 2.1-2.2 coordinate plane and graphs-

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