Comparing Graphing Techniques (Chapter 5.1: GROUP EXPLORATION) Group Work #6 1. Consider the equation 4 x + 5 y = 20 . a. Find the slope and the y-­‐intercept. Use these to graph the equation. b. Now find the x-­‐ and y-­‐ intercepts and use these to graph the equation. Yes, it’s the same graph, just a different method of graphing. c. Which method do you prefer? For this graph, it is easier to find both intercepts and graph. 2. Consider the equation y =
2
x − 1 . 5
a. Find the slope and the y-­‐intercept. Use these to graph the equation. b. Now find the x-­‐ and y-­‐ intercepts and use these to graph the equation. Yes, it’s the same graph, just a different method of graphing. c. Which method do you prefer? For this graph, it is easier to graph using the slope and y-­‐intercept. 3. In general, which types of linear equations do you prefer to graph using the slope and the y-­‐
intercept? Which types do you prefer to graph by finding the intercepts? Explain. If the equation is in the form y = mx + b , it will likely be easier to graph using the slope and y-­‐
intercept. We can easily see these values without doing any algebra. Exceptions to this might be if m and b are fractions or decimals that are difficult to graph. If the equation is in the form Ax + By = C , it will likely be easier to graph using the intercepts. Plugging in zero for either x or y leads to a fairly simple equation to solve. Exceptions to this might be if the intercepts have fraction or decimal values that are difficult to graph. 4. Given an equation Ax + By = C , what relationship between A, B, and C guarantees the intercepts will have integer values (rather than fractions or decimals)? If A and B are factors of C, you are guaranteed to have nice integer values for your intercepts. 4 x + 5 y = 20 y=
2
x − 1 5