This document discusses graphs and coordinate planes. It introduces the x-axis, y-axis, and origin of the Cartesian coordinate system. It shows how to plot points and describes the four quadrants. It explains how to find the distance between points, midpoint of a line segment, slope and y-intercept of a line, and intercepts of graphs. It also covers changing equations to standard form, including completing the square, and graphing linear and circular equations.

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MATH 108
Section 2.1-2.2
Coordinate Plane and Graphs

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x axis
y axis
origin
Rectangular/ Cartesian Coordinate System/ Plane

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−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)

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

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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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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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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

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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.

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

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( ) ( )
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−

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( ) ( )
2 2
For the circle 4 1 9, find the intercepts,
if any, of its graph.
x y− + + =

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Change from general form to standard form
(by completing the square):
x2
+ y2
– 8x + 4y – 5 = 0
x2
+ y2
+ 2x + 6y – 26 = 0