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Investigation Slope Intercept Form: 𝒚 = 𝒎𝒙 + 𝒃 You will be using an online graphing calculator to explore the graph of an equation in the form 𝑦 = 𝑚𝑥 + 𝑏. Please go to the following website and then click the link for the Free Online Graphing Calculator. http://www.rentcalculators.org/stheli.html CLICK HERE!!! Part 1 In Y1 type the equation 𝑦 = 𝑥 + 1 (you don’t need the y = ) In Y2 type the equation 𝑦 = 2𝑥 + 1 (you don’t need the y = ) 1 In Y3 type the equation 𝑦 = (2) 𝑥 + 1 (you don’t need the y = ) Now hit the red GRAPH button and your graphs will appear and they are color coded!!! Use these graphs to answer the following questions: 1. Which graph is closest to the y-axis? ______________________ 2. Which graph is closest to the x-axis? ______________________ 3. What is different in each of the three equations? _______________________________________ 4. Explain how changing the m affects the graph of an equation in the form 𝑦 = 𝑚𝑥 + 𝑏. ________________________________________________________________________________ ________________________________________________________________________________ 5. Use what you learned in #1-4 to match each equation with the best choice for its graph. Part 2 6. Graph these equations on the same screen. 𝑦 = 2𝑥 + 1 𝑦 = −2𝑥 + 1 Explain how the sign of m affects the graph of an equation. _________________________________ ________________________________________________________________________________ ________________________________________________________________________________ 7. Graph these equations on the same screen. 𝑦 = 2𝑥 + 1 𝑦 = 2𝑥 − 2 𝑦 = 2𝑥 + 2 Where does the graph of each equation cross the y-axis? __________________________________ ________________________________________________________________________________ 8. Match each equation with the best choice for its graph. 9. Use all the graphs we have used to answer the following question. Explain how changing the value of b affects the graph of an equation in the form 𝑦 = 𝑚𝑥 + 𝑏. ________________________________________________________________________________ ________________________________________________________________________________ 10. You can change the appearance of a graph by changing its scale in SETTINGS tab. Describe how the graph of 𝑦 = 2𝑥 + 1 changes from its appearance on a standard screen using the following values for Xmin, Xmax, Ymin and Ymax.