Four representations of equations of lines from….. graphs, tables, equations and stories

WARM UP Write the equation of a line given m = - 4 and the point (1, 3). Find the equation of a line from the points (1, 5) and (-2, -4). Graph the equation of the line y = - 𝟏 𝟑 x – 2. A swimming pool is being drained. The table shows the volume of water, y, in cubic feet, after x minutes of draining. a. Write an equation that can be used to model this situation. b. What does the slope mean in context of the situation? c. What does the y-intercept mean in context of the situation? x y 1 8000 2 7500 3 7000 4 6500 5 6000

Today we will be looking at equations of lines using four representations: Tables Graphs Equations Situations – verbal description (scenarios) We will see how we can use one or more of the above to write an equation and then answer questions about the equation. Let’s look at the four representations carefully.

Verbal description (a situation) Communicates in words a situation. From within the description, there is an equation that can be written. Example: A car repairman charges a $25 service fee to look at an automobile. He charges an additional $20 for each hour while he is working on the car.

Given an Equation (y = mx + b) This is when you are given the equation in slope intercept form. You will need the equation to answer questions about the slope and the y-intercept and maybe even to predict something. Use y = mx + b (equation of a line) y = -3x + 5

A Table (T- Chart) If you are given a table, use the points on the table to find the equation of the line: 𝑥 1 , 𝑦 1 𝑎𝑛𝑑( 𝑥 2, 𝑦 2 ) You may need this equation to answer questions or to graph the data.

A Graph Using the situation, table or equation, you may be asked to plot points on a grid and graph your equation. You will then need to use your graph and find information to answer questions.

Answering questions from the table, graph and equation. Once you have an equation, a graph and a table, you will be able to answer questions such as: State the slope and interpret its meaning in context to the situation. What is the y-intercept and what does it mean? You will be able to plug in an “x” value and a “y” and find out additional information – predictions.

Let’s try this one…… The table shows the number of books read monthly by Miss Jones’ class. X (month) Y (number of books) 4 110 5 130 6 150 7 170

Steps to follow: Write the equation of the line from the table. (how would you do that?) Plot the points on a graph. (where do you start graphing from?) Identify and interpret the slope and y-intercept. Answer the questions that follow.

Questions to answer…. What is the slope and what does it mean in context with this story? What is the y-intercept? Interpret the y-intercept. How did you find the y-intercept? (mention all ways) Assuming the number of books read grew at a steady rate throughout the year, what was the number of books read in the 10th month? 12th month? How many books were read in month one? In what month were 210 books read?

CLASSWORK PART ONE….. With your elbow partner, complete the activity called: Representing Linear Equations. Look at the three types of representations of equations of lines and match them. (equation, table and graph)

CLASSWORK PART TWO Now you will work in groups. Each person in your group will be given a situation. You will be responsible for completing the problem. You will have about 10 minutes. After the ten minutes are up, you will each have an opportunity to discuss your situation with your group. You will record the answers for all situations and place this sheet in your binder in the classwork section.

HOMEWORK Complete the worksheet with the different representations of equations. Show all your work. Look back at your notes if you need help.

HOMEWORK HELP http://mymathuniverse.com/programs/cmp3/channels/12/channel_content_items/133 http://www.projectsharetexas.org/resource/connecting-multiple-representations-linear-functionsontrack-algebra-1-module-4-lesson-4 https://learnzillion.com/lessons/290-compare-distance-time-graphs-with-distance-time-equations