Name Date Class Period Activit 8.5 Investigating Slope-Intercept Form MATERIALS QUESTION pencil straightedge graph paper How can ou relate slope, -intercept, and an equation? You can find the slope and -intercept of a line b looking at its equation in slope-intercept form. EXPLORE Use a graph to find the slope and -intercept of = 4+ 3. STEP 1 Complete a table Complete the table of values for the equation = 4 + 3. 0 1 2 1 of 6
STEP 2 Plot points Plot the points from the table in Step 1 in the coordinate grid provided. Then connect the points to draw a line. STEP 3 Find the slope and -intercept Use the graph to find the slope and -intercept of = 4 + 3. Record our results in the table below. Equation Slope -intercept = 4 + 3 = -2-1 = 3 + 5 STEP 4 Complete the table Repeat Steps 1-3 for the other equations in the table. DRAW CONCLUSIONS Use our observations to complete these eercise 1. Use the table in Step 3 to make a conjecture about how to use the equation of a line to find the slope and -intercept of the line. Based on our results from Eercise 1, determine the slope and -intercept of the graph of the equation. Check our answer b following the procedure in the Eplore. 2. = 5-7 3. = -3 + 2 4. = 2 2 3-6 5. = 5 4 + 1 6. What does m represent in the equation = m + b? What does b represent in the equation = m + b? 2 of 6
ANSWER KEY STEP 1 = 4 + 3 = -2-1 = 3 + 5 0 3 0-1 0 5 1 7 1-3 1 8 2 11 2-5 2 11 STEP 2 Check students graphs. STEP 3 Equation Slope -intercept = 4 + 3 4 3 = -2-1 -2-1 = 3 + 5 3 5 DRAW CONCLUSIONS 1. 2. 3. 4. When a linear equation is written as = m + b, the slope is the coefficient of, and the -intercept is the constant term. slope: 5; -intercept: 7 slope: 3; -intercept: 2 slope: 2 ; -intercept: 6 3 3 of 6
5. slope: 5 4 ; -intercept: 1 6. m is the slope; b is the -intercept. 4 of 6
Teacher Notes ACTIVITY PREPARATION AND MATERIALS Make sure each student has a sheet or two of graph paper. You ma want to have some of our own materials, such as a ardstick, chalk, or dr erase markers read to demonstrate different steps of this activit on the board, if necessar. Students will benefit most from working individuall or in pairs. ACTIVITY MANAGEMENT As a review, discuss with students how to find the slope and -intercept of an equation from its graph in a coordinate plane. Common Error Watch for students who switch the values of and when graphing equations. A-Level Alternative Students can work in pairs, or do Steps 1-3 as a class before students do Step 4 on their own. C-Level Alternative Ask students to use the conjecture the wrote in Eercise 6 and the observations the made in this activit to write an equation given its slope and -intercept. You can take student suggestions for these two values and then ask the class to write the equation. Repeat for two or three more equations. For eample, if a student suggests a slope of 8, and a -intercept of 3, then the equation will be = 8 + 3. 5 of 6
Activit and Closure Questions Discuss these questions as a class. 1. Find the slope and -intercept of the graph of = 3-12. Answer: the slope is 3 and the -intercept is -12. 2. What are two was ou can find the slope and -intercept of the graph of the equation = 1 4 8? Answer: You can use the equation to see that the slope is 1 and the -intercept is 8. You could 4 also graph the equation, find the rise and the run, and use the equation slope = rise to find the run slope of 1. To find the -intercept, ou can look to see where the graph crosses the -ais. 4 3. Stacie sas that in the equation 2 = 8 + 12, the slope is 8 and the -intercept is 12. Wrong! How is this equation different from the others? How can ou rewrite the equation so that ou can use it to find the slope and the -intercept? Answer: The equation 2 = 8 + 12 is not in the form = m + b. Multipl the equation b 1 2, or divide it b 2, and rewrite the equation as = 4 + 6 to find the slope is 4 and -intercept is 6. 4. How could ou find the slope and -intercept of the graph of 3 + 2 = 6? Answer: Solve the equation for and use the equation to find the slope and -intercept of the graph of the equation. LESSON TRANSITION After completing the activit, students will be familiar with the concept of finding slopes and -intercepts in Eample 1. After formall introducing the slope-intercept form of an equation, ou ma want to skip Eample 1 and continue the lesson with Eample 2. 6 of 6