Let's plot the given points on graph paper and examine their relationships. Here are the coordinates provided:
- (1, 5)
- (2, 8)
- (3, 11)
- (4, 14)
- (5, 17)
### Step-by-Step Solution:
1. Create the Coordinate Axes:
Draw a horizontal axis (x-axis) and a vertical axis (y-axis) on your graph paper. Label the x-axis with values 1 through 5 and the y-axis with values from 5 to 17.
2. Plot the Points:
- Locate the first point (1, 5). Start at the origin (0,0), move 1 unit to the right and 5 units up. Place a dot at this position.
- For the second point (2, 8), start at the origin, move 2 units to the right and 8 units up. Place a dot at this position.
- Continue this process for the remaining points:
- (3, 11): 3 units to the right and 11 units up.
- (4, 14): 4 units to the right and 14 units up.
- (5, 17): 5 units to the right and 17 units up.
3. Join the Points:
After plotting all the points, use a ruler to join the dots sequentially: (1, 5) to (2, 8), (2, 8) to (3, 11), and so on, until you connect the last pair (4, 14) to (5, 17).
4. Observation:
By joining the points, you will observe that they form a straight line. This indicates a linear relationship between the x and y coordinates.
### Mathematical Interpretation:
- Each point (x, y) follows the pattern y = 3x + 2.
- For x = 1: [tex]\( y = 3(1) + 2 = 5 \)[/tex]
- For x = 2: [tex]\( y = 3(2) + 2 = 8 \)[/tex]
- For x = 3: [tex]\( y = 3(3) + 2 = 11 \)[/tex]
- For x = 4: [tex]\( y = 3(4) + 2 = 14 \)[/tex]
- For x = 5: [tex]\( y = 3(5) + 2 = 17 \)[/tex]
Thus, the relationship between x and y is linear, and the points lie on the line described by the equation [tex]\( y = 3x + 2 \)[/tex].
### Conclusion:
When plotted and connected, the points (1, 5), (2, 8), (3, 11), (4, 14), and (5, 17) form a straight line. This indicates a consistent linear relationship between x and y, following the equation [tex]\( y = 3x + 2 \)[/tex].
