note: Enter your answer and show all the steps that you use to solve this problem in the space provided.On a coordinate plane, a line passes through the points left-parenthesis 0 comma 1 right parenthesis, left-parenthesis 2 comma 4 right parenthesis, and left-parenthesis 6 comma 10 right parenthesis.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 points, we can use the concept of similar triangles.
First, let's calculate the slopes between the points:
- Between (0, 1) and (2, 4): slope = (4-1)/(2-0) = 3/2
- Between (2, 4) and (6, 10): slope = (10-4)/(6-2) = 6/4 = 3/2
We have shown that the slope between the first two points is 3/2 and the slope between the second and third points is also 3/2. This confirms that the slope is the same between any two of the three points.
Now, let's calculate the slope of the line passing through these points using any two of the points. We can choose (0, 1) and (6, 10):
slope = (10-1)/(6-0) = 9/6 = 3/2
Therefore, the slope of the line passing through the points (0, 1), (2, 4), and (6, 10) is 3/2.