1.
2.
3.
4.
Objectives:
To find the intercepts
of a graph
To use symmetry as an
aid to graphing
To write the equation
of a circle and graph it
To write equations of
parallel and
perpendicular lines
• As a class, use your
vast mathematical
knowledge to define
each of these words
without the aid of
your textbook.
Graph of an
Equation
Solution Point
Intercepts
Symmetry
Circle
Parallel
Perpendicular
The graph of an
equation gives a
visual representation
of all solution points
of the equation.
The x-intercept of a
graph is where it
intersects the x-axis.
• (a, 0)
The y-intercept of a
graph is where it
intersects the y-axis.
• (0, b)
6
4
y-intercept
2
-5
x-intercept
5
-2
How many x- and y-intercepts can the graph of
an equation have? How about the graph of a
function?
Given an equation, how do you find the
intercepts of its graph?
• To find the x-intercepts, set y = 0 and solve for
x.
• To find the y-intercepts, set x = 0 and solve for
y.
Find the x- and y-intercepts of y = – x2 – 5x.
A figure has
symmetry if it can
be mapped onto
itself by reflection
or rotation.
Click me!
How would an
understanding of
symmetry help you
graph an equation?
When it comes to
graphs, there are
three basic
symmetries:
1. x-axis symmetry: If
(x, y) is on the graph,
then (x, -y) is also on
the graph.
 x, y    x,  y 
When it comes to
graphs, there are
three basic
symmetries:
2. y-axis symmetry: If
(x, y) is on the graph,
then (-x, y) is also on
the graph.
 x, y     x, y 
When it comes to
graphs, there are
three basic
symmetries:
3. Origin symmetry: If
(x, y) is on the graph,
then (-x, -y) is also
on the graph.
 x, y     x,  y 
(Rotation of 180)
Using the partial graph
pictured, complete
the graph so that it
has the following
symmetries:
1. x-axis symmetry
2. y-axis symmetry
3. origin symmetry
The set of all coplanar
points is a circle if
and only if they are
equidistant from a
given point in the
plane.
Find the equation of points (x, y) that are r units
from (h, k).
Standard form of the equation of a circle:
 x  h   y  k 
2
2
(h, k) = center point
r = radius
r
2
The point (1, -2) lies on the circle whose center
is at (-3, -5). Write the standard form of the
equation of the circle.
Find the center and radius of the circle, and then
sketch the graph.
 x  2    y  3
2
2
 25
Convert the given equation to the following
forms:
3
y  6   x  5
4
1. Slope-intercept form
2. Standard form
Convert the given equation to the following
forms:
3 x  7 y  10
1. Slope-intercept form
2. Point-slope form
Two lines are parallel
lines iff they are
coplanar and never
intersect.
m || n
Two lines are
perpendicular lines iff
they intersect to form
a right angle.
Two lines are parallel
lines iff they have the
same slope.
Two lines are
perpendicular lines iff
their slopes are
negative reciprocals.
Write an equation of the line that passes
through the point (-2, 1) and is:
1. Parallel to the line y = -3x + 1
2. Perpendicular to the line y = -3x + 1
1.
2.
3.
4.
Objectives:
To find the intercepts
of a graph
To use symmetry as an
aid to graphing
To write the equation
of a circle and graph it
To write equations of
parallel and
perpendicular lines