What is a linear equation in two variables and how do we graph it? Miller et. al. (2020, p.191) explains that a linear equation in two variables is an equation that can be written in the form, Ax + By = C, where A, E. and C. are real numbers such that A and B are not both zero. Additionally, a solution to such an equation is an ordered pair (at. y") that makes the equation a true statement. To graph a linear equation, there are a few options: I Plotting Points: Find two solution points and draw the line between them. Review Examples 2-4 in Section 10.2 of the Prealgebra 8: Introductory Algebra textbook. - :1- and y intercepts: Find the xintercept and y-intercept and draw the line between them. Review Examples 5-6 in Section 10.2 of the Frealgebra 8: Introductory Algebra textbook. - Slope and y-intercept: From the slopeintercept form, y = mx + b. of a linear equation, plot the y-inbercept and. then plot the slope irorn the y-intercept. Review Examples 34% in Section 10.4 of the Frealgebra 81 Introductory Algebra textbook. Algebraic Investigations Each of the following algebraic investigations is looking at different graphs of equations of a line. Use the Geogebra ll?" graphing calculator to graph the equations. For this discussion, you will choose two of the following algebraic investigations to complete. 1 Expand all 2 Graphing Linear Equations #1 1. Graph and explain what the similarities and differences are between these two graphs: l 2. Write the equation of a line whose slope is '2. for a classmate to graph. Graphing Linear Equations #2 1. Graph and explain what the similarities and differences are between these two graphs: 3 +4- \\!=_I " S 5 +4 J .31 2. Write the equation of a line whose y-intercept is (O, 2) for a classmate to graph. Graphing Linear Equations #3 Graphing Linear Equations #4 @ Instructions 1. Review the rubric to make sure you understand the criteria for earning your grade. 2. Read sections 10.1 to 10.6 in your textbook: Prealgebra .5} Introductory Algebra. 3. Choose two of the algebraic investigation problems described above. a. Post two initial discussion posts, one for each algebraic investigation, by the end of the fourth clay. b. 1n the subject box of your initial post, identify which investigation you are addressing. c. In your initial post, include the instructions addressing all of the prompts and questions, your solutions or answers to all of the questions. showing your work and explaining . Make sure to post the equation for a classmate to graph. Make sure you know the answer so that you can. check any classmate's work who responds to your initial post. 4. Respond to two other classmates' posts and/or instructor posts by the endrof the workshop. a. For classmates' posts, make sure your response includes the graph of the equation oF a line your classmate has created for you to solve. Show all of your work and explain your solutions or answers. b. For Instructor posts. make sure your response addresses your instructor's questions in a manner that ' Msllllft , ' provides evidence