Algebra
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Graphing points, equations and inequalities
Understanding the coordinate plane, slope, and intercept. Writing, solving, and graphing linear equations and inequalities.
Coordinate plane
How can we communicate exactly where something is in two dimensions? Who was this Descartes character?
In this tutorial, we cover the basics of the coordinate plane. We then delve into graphing points and determining whether a point is a solution of an equation. This will be a great tutorial experience if you are just starting to ramp up your understanding of graphing or need some fundamental review.
Graphing solutions to equations
In this tutorial, we'll work through examples that show how a line can be viewed as all of coordinates whose x and y values satisfy a linear equation. Likewise, a linear equation can be viewed as describing a relationship between the x and y values on a line.
- Ordered pair solutions of equations
- Ordered Pair Solutions of Equations 2
- Plotting (x,y) relationships
- Graphs of Linear Equations
- Application problem with graph
- Ordered pair solutions to linear equations
- Interpreting Linear Graphs
- Exploring linear relationships
- Recognizing Linear Functions
- Identifying linear relationships
- Graphing lines 1
Graphing lines using x and y intercepts
There are many ways to graph a line and this tutorial covers one of the simpler ones. Since you only need two points for a line, let's find what value an equation takes on when x = 0 (essentially the y-intercept) and what value it takes on when y = 0 (the x-intercept). Then we can graph the line by going through those two points.
Slope
If you've ever struggled to tell someone just how steep something is, you'll find the answer here. In this tutorial, we cover the idea of the slope of a line. We also think about how slope relates to the equation of a line and how you can determine the slope or y-intercept given some clues.
This tutorial is appropriate for someone who understands the basics of graphing equations and want to dig a bit deeper. After this tutorial, you will be prepared to start thinking deeper about the equation of a line.
Equation of a line
You know a bit about slope and intercepts, but want to know more about all the ways you can represent the equation of a line including slope-intercept form, point-slope form, and standard form.
This tutorial will satisfy that curiosity!
- Graphing a line in slope intercept form
- Converting to slope-intercept form
- Graphing linear equations
- Linear Equations in Slope Intercept Form
- Graphs Using Slope-Intercept Form
- Word Problem Solving 4
- Equation of a line 1
- Equation of a line 2
- Equation of a Line hairier example
- Equation of a line 3
- Solving for the y-intercept
- Slope intercept form
- Linear Equations in Point Slope Form
- Point slope form
- Linear Equations in Standard Form
- Point-slope and standard form
- Converting between slope-intercept and standard form
- Converting between point-slope and slope-intercept
- Finding the equation of a line
- Equations from tables
- Fitting a Line to Data
More analytic geometry
You're familiar with graphing lines, slope and y-intercepts. Now we are going to go further into analytic geometry by thinking about distances between points, midpoints, parallel lines and perpendicular ones. Enjoy!
- Midpoint Formula
- Midpoint formula
- Distance Formula
- Distance formula
- Perpendicular Line Slope
- Equations of Parallel and Perpendicular Lines
- Parallel Line Equation
- Parallel Lines
- Parallel Lines 2
- Parallel lines 3
- Perpendicular Lines
- Perpendicular lines 2
- Equations of parallel and perpendicular lines
- Distance between point and line
- Algebra: Slope and Y-intercept intuition
- Algebra: Equation of a line
- CA Algebra I: Slope and Y-intercept
Graphing linear inequalities
In this tutorial we'll see how to graph linear inequalities on the coordinate plane. We'll also learn how to determine if a particular point is a solution of an inequality.
- Graphing Inequalities
- Solving and graphing linear inequalities in two variables 1
- Graphing Linear Inequalities in Two Variables Example 2
- Graphing Inequalities 2
- Graphing linear inequalities in two variables 3
- Graphs of inequalities
- Graphing linear inequalities
- Graphing Inequalities 1
- Graphing and solving linear inequalities
- CA Algebra I: Graphing Inequalities