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Graphing Equations

Graphing Equations

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Author: Corey Felber
Description:

CCSS.Math.Content.8.F.A.2 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

CCSS.Math.Content.8.F.B.5 - Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

I am targeting a Junior High School audience mainly grade levels 7 or 8.

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Tutorial

Graphing Equations Using Slope-Intercept Form

This video gives a step-by-step example of how to find the intercepts and slope in order to graph the specific linear equation.

Linear Equations

In order to teach students about graphing linear equations, I first must give an example of the slope-intercept form of a linear equation.  That is: y=mx+b.  Where m is the slope and b is the y-intercept.  Slope-intercept form is most necessary when graphing equations.

Equation: 2x+3y=12

Notice that this equation is not in slope-intercept form.

http://www.charleston.k12.il.us/cms/Teachers/math/PreAlgebra/paunit6/L6-1.PDF

-Students can use this link as an aid with selected examples of converting to slope-intercept form.

What Does Slope-Intercept Form Tell Us?

Now, the idea of slope-intercept form holds all the keys that we need in order to graph any equation.

Note: b = y-intercept (in other words, where the graph crosses the y-axis)

Note: m = slope (in other words, it tells us where to put the points that will make up our line)

This link will allow for more in depth instruction on graphing the slope of each line.

-http://www.algebra-class.com/graphing-slope.html

Different Ways to Graph Equations

It is important to understand that graphing equations using slope-intercept form is not the only way to graph equations; that was only the purpose of this presentation.  This video describes an alternative way to graph basic linear equations without using slope-intercept form.

https://www.youtube.com/watch?v=m_mRQT7pUUw

Note that any method chosen will produce the same graph.  Depending on the problem, it may be beneficial to choose one instead of the other.

Graphing Equations by Making a Table (additional ex)

Here an equation is graphed by making a table.

The "BIG Question"

As you have learned from the presentation, graphing equations can be very beneficial in solving mathematical problems.  We have learned that there are different methods to graphing equations and that some may be easier but they all produce the same graph.  The Big Question I want you to think about is:

 

What can the information provided in graphs tell us about the equations that are being graphed?