If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the line?
Practice Questions
1 question
Q1
If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the line?
1
2
0
undefined
Slope = (4-2)/(3-1) = 1, and it remains the same for other points.
Questions & Step-by-step Solutions
1 item
Q
Q: If the points (1, 2), (3, 4), and (5, 6) are collinear, what is the slope of the line?
Solution: Slope = (4-2)/(3-1) = 1, and it remains the same for other points.
Steps: 11
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.
