- Topics At a Glance
- Arithmetic, Geometric & Exponential Patterns
- Algebraic Expressions
- Evaluating Algebraic Expressions
- Combining Like Terms
- Distributive Property
- Multiplying Monomials
- Multiplying Binomials
- Dividing Polynomials
- Graphing X-Y Points
- Solving One-Step Equations
- Solving Two-Step Equations
- Solving More Complex Equations
- Solving Equations with Variables on Both Sides
- Solving Funky Equations
- Graphing Inequalities
- Solving Inequalities
- Graphing Lines
- Intercepts
- Graphing Horizontal & Vertical Lines
- Graphing Lines By Plotting Points
- Slope-Intercept Form
- Solving Multiple Equations by Graphing
Introduction to Graphing X-y Points:
Graphing X-Y Points
Chances are you have been graphing points for a long time. However, you may have been doing so on charts that look like this:
But since you are blasting ahead in math, you soon will be graphing on charts that look like this:
This is called a Cartesian coordinate graph. It is made up of two axes ("axes" is simply the plural of "axis"):
- The horizontal axis is called the x-axis.
- And the vertical one is the y-axis.
When the two axes meet they form four quadrants. These are labeled as quadrants 1-4 (usually shown in roman numerals) and are ordered counterclockwise starting from the upper right quadrant.
Plotting Points on a Graph
Cartesian points are written as x-y pairs in parentheses (x, y). To graph a point, first locate its position on the x-axis, then find its location on the y-axis and plot where these meet.
The center point of the graph is called the "origin" and is written as the point (0, 0), because it is located at the zero point on the x-axis and the zero point on the y-axis.
For example, to plot the point (3, -6), find the positive three on the x-axis and the -6 on the y-axis.
Give the Cartesian coordinates of each point and name the quadrant they lie in.
A. (5, 3), Quadrant I
B. (-3, 1), Quadrant II
C. (-6, -4), Quadrant III
D. (0, -3), it lies on an axis so it is not in a quadrant
E. (0, 0), no quadrant
F. (4, -5), Quadrant IV
G. (6.5, 0), it lies on an axis so it is not in a quadrant
Graphing X-y Points Practice:
In which quadrant(s) are both the x and y coordinates the same sign?
If a point has a y coordinate of zero, which axis does it lie on?
Do these points lie in a straight line: (-8, -1), (-6, 1), (-4, 3) and (0, 7)?
What type of quadrilateral do these points form: (-3, 1), (4, 1), (2, -2) and (-5, -2)?
