Question

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.

Answer 1

Let's consider the three indicated points: A(2,4), B(4,6), and C(6,8).

To show that the slope of the line between any two of these points is the same, we can use the concept of similar triangles.

First, let's calculate the slope of the line passing through points A and B:
Slope between A and B = (y2 - y1) / (x2 - x1) = (6 - 4) / (4 - 2) = 2 / 2 = 1

Now, let's calculate the slope of the line passing through points B and C:
Slope between B and C = (y2 - y1) / (x2 - x1) = (8 - 6) / (6 - 4) = 2 / 2 = 1

Finally, let's calculate the slope of the line passing through points A and C:
Slope between A and C = (y2 - y1) / (x2 - x1) = (8 - 4) / (6 - 2) = 4 / 4 = 1

Since the slope between any two of these three points is 1, we have shown that the slope of the line is the same between any two of these three points. This demonstrates that the line passing through these points is a straight line.

Therefore, the slope of the line passing through points A(2,4), B(4,6), and C(6,8) is 1.