Exploring the Graph of Section 1: Reviewing the Linear Function Earlier in the course we explored the linear function family, defined by the equation We studied the roles of the parameters and We found that regardless of the numbers used . m b. to replace or our graphs were always straight lines. m b, Before summarizing the roles of and below, refresh your memory by graphing m b = 0.5x + 1, = 2x + 1, and = 4x + 1 and on your calculator. If > 0, what can you say y y y m about the graph of the equation = + y mx b? As increases, what happens to the graphs? Be specific. m Now graph = 0.5x + 1, = + 1, and = 4x + 1 on your calculator. If < 0, what y y y m – –2x – can you say about the graph of the equation = + y mx b? As decreases, what happens to the graphs? Be specific. m Now let = 0 and graph = 0x + 1. How does this graph differ from the graphs in questions m y 1 and 3? Now consider the graphs of = 2x + 3, = 2x + 4 and = 2x 5. How are these graphs y y y – alike? How do the graphs in question 6 differ? Now summarize the roles of the parameters and in the equation m b Without graphing, what can you say about the graph of = 5x + 4? y
Exploring the Graph of Section 1: Reviewing the Linear Function Earlier in the course we explored the linear function family, defined by the equation . We studied the roles of the parameters m and b. We found that regardless of the numbers used to replace m or b, our graphs were always straight lines. Before summarizing the roles of m and b below, refresh your memory by graphing y = 0.5x + 1, y = 2x + 1, and y = 4x + 1 and on your calculator. If m > 0, what can you say about the graph of the equation y = mx + b? As m increases, what happens to the graphs? Be specific. Now graph y = – 0.5x + 1, y = –2x + 1, and y = – 4x + 1 on your calculator. If m < 0, what can you say about the graph of the equation y = mx + b? As m decreases, what happens to the graphs? Be specific. Now let m = 0 and graph y = 0x + 1. How does this graph differ from the graphs in questions 1 and 3? Now consider the graphs of y = 2x + 3, y = 2x + 4 and y = 2x – 5. How are these graphs alike? How do the graphs in question 6 differ? Now summarize the roles of the parameters m and b in the equation Without graphing, what can you say about the graph of y = 5x + 4?