Essay Question: Explain the three different ways to represent linear equations. STEP 1: HOW TO WRITE AN INTRODUCTION STEP 2: HOW TO WRITE THE BODY PARAGRAPHS STEP3: HOW TO WRITE A CONCLUSION Linear Situations

Overview Introduction  Introduce topic in an interesting way (question or anecdote); provide a thesis statement Body Paragraph 1: Tables  Introduce, explain, and provide examples of Tables Body Paragraph 2: Graphs  Introduce, explain, and provide examples of Graphs Body Paragraph 3: Equations  Introduce, explain, and provide examples of Equations Conclusion  Summarize findings from all three body paragraphs; restate thesis

Introduction Interesting lead in (1-2 sentences)  Start with a question or anecdote Thesis (1 sentence)  Address your topic by listing what your body paragraphs will include EXAMPLE: Did you know there are three different ways to represent linear equations? Linear equations are straight lines and can be represented through a table, a graph or an equation.

Body Paragraph 1: Tables Topic sentence (1 sentence)  Identify and define representation: What is a table? How and why to use tables (3-4 sentences):  Answer the question where does it start?  Explain how does it grow?  Provide examples for clarification Clincher Sentence (1 sentence)  Summarize the use of tables

Body Paragraph 1 Example A table, one of the three representations of a linear equation, is simply a chart that contains the x and y values of a linear equation. An example for a table for a linear equation would be: Although we do not know the equation of this linear equation, and do not have a graph, a table still reveals much valuable information. By examining the change in y-values and x-values on the table, we can determine that this graph has a slope of two, meaning that the graph will increase by two on the y- axis for every increment of one on the x-axis. Additionally, the graph tells us that y has a value of four when x has a value of zero, meaning that the y- intercept of the graph is four. Using the information from the table, it can be determined that the graph will start at the point (0,4) and increase by a slope of two from there in both the positive and negative direction. xy

Body Paragraph 2: Graphs Topic sentence (1 sentence)  Identify and define representation: What is a graph? How and why to use graphs (3-4 sentences):  Answer the question where does it start?  Explain how does it grow?  Provide examples for clarification Clincher Sentence (1 sentence)  Summarize the use of graphs

Body Paragraph 2 Example Also, the linear equation can be represented on a graph. The graph of this particular equation would look like: By examining the change in the x and y values, it can be confirmed that our equation has a slope of two, since it increases by two on the y-axis for every increase of one on the x-axis. Also, by finding the point where the line intersects the y-axis, it is confirmed that this graph has a y-intercept of four. Hence, the graph starts at (0,4) and extends from there in either direction according to its slope of two. Using the information from either the table or the graph, an equation to represent this line can be produced.

Body Paragraph 3: Equations Topic sentence (1 sentence)  Identify and define representation: What is an equation? How and why to use equations (3-4 sentences):  Answer the question where does it start?  Explain how does it grow?  Provide examples for clarification Clincher Sentence (1 sentence)  Summarize the use of equations

Body Paragraph 3 Example Finally, an equation for a straight line is expressed in the format y=mx+b. In this equation, “m” is the slope and “b” is the y-intercept. The equation for this particular line would be y=2x+4. This means that the graph begins at (0,4) and increments by two on the y-axis for every increment of one on the x-axis. The equation is another valid way to represent a straight line.

Conclusion Restate thesis from your introduction (1 sentence)  1) Restate the thesis using different words than in your introduction (1 sentence)  2) Review main points (1-2 sentences)  3) Concluding sentence: Provide a final significant thought for the reader (1 sentence) EXAMPLE: In conclusion, all three of the representations provide the necessary information: where the graph starts and how it grows indicating both the slope and y-intercept. Although all three representations are unique, they all succeed at providing the necessary information about where the line starts and how it grows.