Math 22 Graph of Equation

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The Graph of an Equation

The graph of an equation is the set of all points that are solutions of the equation.

In this section, we use point-plotting method. With this method, you construct a table of values that consists of several solution points of the equation

For example, sketch the graph of . We can construct the table below by plugging points for .

x 0 1 2 3
y=2x+1 1 3 5 7

So, we can sketch the graph from those order pairs.

Graph 1.2.png

Intercepts of a Graph

Some solution points have zero as either the -coordinate or the -coordinate. These points are called intercepts because they are the points at which the graph intersects the - or -axis.

 To find -intercepts, let  be zero and solve the equation for .
 To find -intercepts, let  be zero and solve the equation for .

Example Find the x-intercepts and y-intercepts of the function

x-intercept: Let , so , hence , therefore, or
y-intercept: Let , so
Answer: and are x-intercepts
is y-intercept


 The standard form of the equation of a circle is
 The point  is the center of the circle, and the positive number  is the radius of the circle

In general, to write an equation of a circle, we need to know radius and the center .

Example Given that the point is on the circle centered at (3,4). Find the equation of a circle.

We need to know the radius and the center in order to write the equation. The center is given at . It is left to find the radius.
Radius is the distance between the center and a point on the circle. So, radius is the distance between and .
Now, write the equation of the circle with radius and center to get:


Distance between and can be calculated by using

Points of Intersection

An ordered pair that is a solution of two different equations is called a point of intersection of the graphs of the two equations

For example, find the point(s) of intersection of two equations and .

The order pairs that satisfy both of these equation should have the same value, so



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This page were made by Tri Phan