Question 36

Question 36 Mr. Perry’s students used pairs of points to find the slopes of lines. Mr. Perry asked Avery how she used the pairs of points listed in this table to find the slope of a line. Avery said, “the easiest way to find the slope is to divide y by x. The slope of this line is 18/8 or 9/4. x y 8 18 20 45 The students can use calculators for this problem. In this first part, the student is saying that you can just divide the y by the x and get the value you are looking for. This might not always be the case, as seen in Part B of this problem.

Question 36 Part A Show another way to find the slope of the line that passes through the points listed in the table. Your way must be different from Avery’s way. 𝑚= 27 12 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 Most of the students are taught to find the slope of the line by using the formula: m = (y2 – y1)/(x2 – x1), where (x1, y1) is a coordinate and (x2, y2) is a coordinate. To solve this, we plug in the following points. The first coordinate will be (8, 18) so x1 will be 8 and y1 will be 18. The second coordinate will be (20, 45) where x2 will be 20 and y2 will be 45. You plug in the numbers to start to solve for the slope. You then simplify what you have done. 45 – 18 is 27 and 20 – 8 is 12. So you get 27/12. You can simplify this by dividing the top and bottom by 3, getting 9/, which is the same that Avery got. 𝑚= 9 4 𝑚= 45−18 20−8

Question 36 Part B Write an example that shows that Avery’s “divide y by x” method will not work to find the slope of any line. Avery’s method does not always work to find the slope of the line. If, for example, the points were (1, 1) and (2, 3), when you use the slope formula, you get the slope is 2. But, in Avery’s method she would get two different slopes: 1 and 1.5, neither of which are the correct answer. Avery’s method does not always work to find the slope of the line. If, for example, the points were (1, 1) and (2, 3), when you use the slope formula, you get the slope is 2. But, in Avery’s method she would get two different slopes: 1 and 1.5, neither of which are the correct answer.