Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Using the three indicated points on the given line and the concept of similar triangles, show and explain why the slope of the line is the same between any two of these three points. Calculate the slope of the line.
To show that the slope of the line is the same between any two of the three indicated points (2,1), (4,4), and (6,7), we can use the concept of similar triangles.
First, we need to calculate the slope between the points (2,1) and (4,4):
m = (y2 - y1) / (x2 - x1)
m = (4 - 1) / (4 - 2)
m = 3 / 2
Next, we calculate the slope between the points (4,4) and (6,7):
m = (y2 - y1) / (x2 - x1)
m = (7 - 4) / (6 - 4)
m = 3 / 2
Since the slopes between (2,1) and (4,4) as well as between (4,4) and (6,7) are both 3/2, we have shown that the slope of the line is the same between any two of the three points.
To calculate the slope of the line passing through these three points, we can use any two points. Let's choose (2,1) and (4,4):
m = (4 - 1) / (4 - 2)
m = 3 / 2
Therefore, the slope of the line passing through the points (2,1), (4,4), and (6,7) is 3/2.