Sharing is Caring: Linear Equations Review

Going forward, I plan to share various presentations, worksheets, or other resources I created for use with my students.  Some will focus on AP Calculus, but most will focus on algebra 1, or its prerequisites.  I know my students benefit greatly when I leverage existing material found on the World Wide Web and adapt it to their needs.  Perhaps others may benefit from mine.

My first share consists of excerpts of a presentation I created to review the key characteristics of linear equations as well as how to graph linear equations that are in slope-intercept form.

I will post the entire presentation, or a link to it, when I figure out how best to do so without requiring too much storage space from my WordPress account.

Reviewing Linear Equations

The following slides were excerpted from a thirteen slide presentation.  I purposely used different colors when representing slope (green), the y-intercept (red), the dependent variable y (blue), and the independent variable x (purple).  Consistent use of the colors through the presentation helped some students zero in on specific parameters such as slope.  At the same time, one student, who I expected to resonate with the colors, as he loves to doodle with various colored markers, commented that there were too many colors.  Oh well, you win some, you lose some.

linear equation, slope-intercept form of a line

Note that I included many synonyms for each parameter above.  I use these interchangeably with students and encourage them to do the same.  As a former engineer, with a physics credential, and as an AP Calculus teacher, I want all of my algebra 1 students to understand the many ways we describe a linear equation.

linear equation, slope-intercept form of a line

Not to diminish the importance of the y-variable (output) or the x-variable (input), this slide directs students’ focus to the key parameters in the slope-intercept form of a line: slope (m) and y-intercept (b), as these provide the key information needed to graph the linear equation.

The following two slides provide step-by-step guidance on how to graph a line when it is in slope-intercept form.  The first is generalized for any line, y = mx + b, while the second is a specific example.

graphing, linear equations, slope-intercept form

graphing, linear equations, slope-intercept form of a line

The complete presentation includes similar examples as well as how to graph a linear equation using a t-table, how to write the linear equation for a line between two points using the point-slope form of a line, and how to interpret the slope of a line from a graph.

I hope this is helpful to one or two mathematics teachers out there somewhere!


About Dave aka Mr. Math Teacher

Secondary math teacher teaching math intervention, algebra 1, honors precalculus, and AP Calculus AB. I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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7 Responses to Sharing is Caring: Linear Equations Review

  1. mrdardy says:


    Thanks for sharing this – I look forward to the link and I’ll share it out to my Algebra teachers.


  2. Jim says:

    I can’t help but wonder whether these slides are throwing too much information at one time at students to whom all these concepts are totally new. It strikes me that they might be better for a review lesson than the initial plunge into the water.


    • You are right on, Jim. Please note the title to this post. 🙂

      In all seriousness, my attempt to build up this knowledge took a ridiculous number of days. Even then, less than half of my students got it. The density of these slides summarized and connected everything I taught to build understanding. I used the whiteboard for all of those efforts. Perhaps I need to create slides for that as well.


  3. Jim says:

    I’m sorry, my eyes skipped over the title. You clearly indicate that they are for review. My apologies.


  4. Tom Neal says:

    Excellent summary of the linear equation process. We are this point in the year and I like your “different color” approach. This will be helpful. Thanks.


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