Ch 1 Section 1
Introduction to Graphing Equations
Watch this video to complete this section.
The Cartesian Plane
The rectangular coordinate system that consists of:
• a horizontal line called the ___________________
• a vertical line called the __________________
• their point of intersection called the ______________
The Cartesian Plane is divided into 4 Quadrants.
a) Locate each of the 4 Quadrants.
b) Locate the Origin.
c) Locate the x and y-axis.
Example 1
Plot the each of the following on the Cartesian Plane.
a) (−2, 3)
b) (1, −4)
c) (0, 2)
Ordered Pair Solutions
An ordered pair is a solution to an equation if when plugged in to the equation, it makes a true
statement.
Example 2:
Example 2 Video Link
Given the equation 𝑦 = 𝑥 2 + 5𝑥 + 4
a) Determine whether or not (0,4) is an ordered pair solution.
b) Determine whether or not (–1, 1) is an ordered pair solution.
a) Use the “Table” feature on a graphing calculator to find 3 other ordered pair solutions.
c) Graph the equation by plotting points.
Example 3:
Example 3 Video Link
Given the equation 2𝑥 2 + 𝑦 = 4
b) Determine whether or not (0, 3) is an ordered pair solution.
c) Determine whether or not (–1, 2) is an ordered pair solution.
d) Use the “Table” feature on a graphing calculator to find 3 other ordered pair solutions.
e) Graph the equation by plotting points.
Adjust Window Settings
Using the above example, change the window settings as described below. How does this affect
the image?
X minimum = −4 X maximum = 4 X scale = 2
Y minimum = −5 Y maximum = 6 Y scale = 1
Example 4:
Example 4 Video Link
Determine the viewing window that is being used in the image below.
Standard Viewing Window:
X minimum = −10 X maximum = 10 X scale = 1
Y minimum = −10 Y maximum = 10 Y scale = 1
X and Y Intercepts
An x-intercept is where the graph touches or crosses the x-axis.
A y-intercept is where the graph touches or crosses the y-axis.
Example 5:
Example 5 Video Link
Determine the x and y intercepts of the following graph.
Notice:
On an x-intercept, the y-coordinate of the ordered pair is 𝑦 = 0.
On a y-intercept, the x-coordinate of the ordered pair is 𝑥 = 0.
Example 6:
Example 6 Video Link
A movie theater offers a monthly membership for avid movie lovers. The graph below shows
the relation between the monthly cost C and the number of movies seen m.
a. What is the cost of watching 5 movies in a month? 10 movies?
b. What is the cost of watching 25 movies in a month?
c. Identify and interpret the intercept.
