If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the

If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the line?

If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the line?

Correct Answer: 1

Step 1: Identify the points given in the question. The points are (1, 2), (3, 4), and (5, 6).
Step 2: Understand that to find the slope of a line through two points, we use the formula: Slope = (y2 - y1) / (x2 - x1).
Step 3: Choose the first two points to calculate the slope. Let's use (1, 2) and (3, 4). Here, (x1, y1) = (1, 2) and (x2, y2) = (3, 4).
Step 4: Substitute the values into the slope formula: Slope = (4 - 2) / (3 - 1).
Step 5: Calculate the difference in y-coordinates: 4 - 2 = 2.
Step 6: Calculate the difference in x-coordinates: 3 - 1 = 2.
Step 7: Now, divide the difference in y by the difference in x: Slope = 2 / 2.
Step 8: Simplify the fraction: 2 / 2 = 1.
Step 9: Since the points are collinear, the slope between any two points will be the same. We can check the slope between (3, 4) and (5, 6) to confirm.
Step 10: Using (3, 4) and (5, 6), we find: Slope = (6 - 4) / (5 - 3) = 2 / 2 = 1.
Step 11: Therefore, the slope of the line through the points (1, 2), (3, 4), and (5, 6) is 1.

Collinearity – Understanding that points are collinear if they lie on the same straight line, which can be determined by calculating the slope between any two points.
Slope Calculation – The slope of a line is calculated using the formula (y2 - y1) / (x2 - x1) for any two points (x1, y1) and (x2, y2).