Paul Torfs and Claudia Brauer not so short introduction More locally, I have taken tutorials originally written by Roger Ratcliff and various graduate students on how to do analysis of variance using S and adapated them to the R environment. This guide was developed to help others learn R, and also to help students in Research MethodsPersonality ResearchPsychometric TheoryStructural Equation Modelingor other courses do some basic statisics. To download a copy of the software, go to the download section of the cran.
Warm Up 10 minutes Have students work to graph these three equations in any way they would like slope-intercept method, using intercepts, making a table, etc.
Students will notice rather quickly that all three are representative of the same equation. The question is why? Let students work in pairs to determine why all of these equations are actually the same MP3.
Some students will use algebraic manipulation to show why they are the same. Others may reason about it by using values for x and y MP2. In either case, we are planting the seeds to have students be able to write equations in a variety of ways and noticing that their structure can give clues as to the way an equation will appear for example, slope-intercept form For this activity, the outcomes may be very open ended.
Try to call on students to share their results that will offer explanations that are insightful but not confusing. There will be more time spent in future lessons on writing functions in certain forms.
In each of these examples, students will be identifying the rate of change and y-intercept in context and using their mathematical model to answer a predictive question. If time permits, have students use the document camera to show their solutions to a particular quesiton and allow their classmates to ask questions about their work.Linear and Quadratic Functions Linear Functions We now begin the study of families of functions.
Our rst family, linear functions, are old friends as Write the equation of the line containing the points (1;3) and (2;1). positive slope was called an increasing line because a linear function with m>0 is an increasing function.
Find the linear equation of a line using the point-slope form, slope-intercept form, two-point form, two-intercept form, etc. Also presented here are worksheets where children will have to find the equations of a line that are either parallel or perpendicular to another line.
Using a Table of Values to Graph Linear Equations You can graph any equation using a table of values. A table of values is a graphic organizer or chart that helps you determine two or more points that can be used to create your graph.
Using table or graph write a linear function that relates y to x. For the Graphs, determine if the domain is discrete or continuos. Graphing linear equations is pretty simple, but you'll reliably get correct answers (that is, you'll reliably draw good graphs) only if you do your work neatly.
If you're messy, you'll often make extra work for yourself, and you'll frequently get the wrong answer. Students learn to write the equation of a line in slope-intercept form using a table of ordered pairs. The first step is to determine if the ordered pairs in the table lie on a line, so that slope-intercept form, or y = mx + b form, can be used to write the equation of the line.