Introduction
In this lens you will learn how to graph linear equations. There are three primary techniques used to graph linear equations. They are:
1) T-Chart - A list of points found by substituting values in for x and find the corresponding y values.
2) Slope-Intercept Method - A very common technique that starts by solving for y and then using the equation to help find the slope and y-intercept of the graph.
3) Intercept Method - A very quick way of determining two points (the x and y intercepts). It is particularly useful when the equation is in standard form.
If you are a teacher looking for resoureces check out my math teaching website. There are some very good worksheets. If you are looking for more math videos check out my videos on youtube.
If you are a student and looking to get all of your math help in one place this math learning site is for you.
1) T-Chart - A list of points found by substituting values in for x and find the corresponding y values.
2) Slope-Intercept Method - A very common technique that starts by solving for y and then using the equation to help find the slope and y-intercept of the graph.
3) Intercept Method - A very quick way of determining two points (the x and y intercepts). It is particularly useful when the equation is in standard form.
If you are a teacher looking for resoureces check out my math teaching website. There are some very good worksheets. If you are looking for more math videos check out my videos on youtube.
If you are a student and looking to get all of your math help in one place this math learning site is for you.
Understanding Graphs of Linear Equations
The most important thing for any student to understand about linear equations is what the line represents. The graph of a linear equation is the collection of all points (x, y) that make the equation true. Another name for those points are solutions to the equation. Linear equations are unique because all of the solutions lie on the same straight line. We use that information to help us develop the three methods for graphing linear equations that are discussed here. The first is graphing linear equations using a T-Chart. Since all of the solutions lie on the line it is sufficient to find a few of them and then draw a line through the points. Usually it is a good idea to find at least three points to insure the accuracy of your calculations. Check out the videos below to help flesh out the technique.
Video Tutorials on Graphing Equations Using a T-Chart
These videos will help you master the technique of graphing linear equations using a T-Chart.
curated content from YouTube
The Slope-Intercept Method
The slope-intercept method is an important technique for graphing linear equations. Its value is more than just the ability to graph equations. Rather it allows us to describe situations in terms of a rate (m - slope) and a constant (b - y intercept). Below is a quick algorithm for using this method. Below that are some videos giving more detailed explanations.
Algorithm
1) Always solve the equation for y first.
2) Once the equation is solved for y, then rearrange the other side to look like y = mx + b, where m represents the slope of the equation and b represents y-coordinate of the y-intercept.
3) Graph the y-intercept.
4) Find the next point by using the slope and the fact that it slope is rise/run.
5) Find at least one more point using the slope.
6) Connect the dots to represent the line.
Algorithm
1) Always solve the equation for y first.
2) Once the equation is solved for y, then rearrange the other side to look like y = mx + b, where m represents the slope of the equation and b represents y-coordinate of the y-intercept.
3) Graph the y-intercept.
4) Find the next point by using the slope and the fact that it slope is rise/run.
5) Find at least one more point using the slope.
6) Connect the dots to represent the line.
Graphing Using the Intercept Method
A third way to graph lines is to use the intercept method. The intercept method recognizes that every straight line crosses both the x-axis and the y-axis. Thus, identifying those two points are sufficient for graphing the lines. For many this is the preferred method of graphing because it is very simple to find the these two points. Essentially, the x-intercept occurs when the y-coordinate is 0 and the y-intercept occurs when the x-coordinate is 0. Thus it is just a matter of plugging in 0 for y and solving for x and then plugging in 0 for x and solving for y.
A Review of Slope
When considering graphs of linear equations it is always essential to understand how to calculate slope and what it means about the graphs of linear equations. The following videos will give you a good look at slope.
curated content from YouTube
Graphing Calculators are an Essential Tool for Algebra
by MrT68
My name is Trent Tormoehlen and I am a math teacher at Sycamore School in Indianapolis Indiana. I will also be helping coach the schools Math Counts... more »
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