Let's solve the problem step by step.
We are given pairs of points (Point A and Point B), and we need to:
1.
Find the change in x (Δx):
$$
\Delta x = x_B - x_A
$$
2.
Find the change in y (Δy):
$$
\Delta y = y_B - y_A
$$
3.
Find the gradient (slope):
$$
\text{Gradient} = \frac{\Delta y}{\Delta x}
$$
Let’s go through each row one by one.
---
Row 1:
- Point A: (4, 9)
- Point B: (5, 11)
- Δx = 5 - 4 =
+1
- Δy = 11 - 9 =
+2
- Gradient = $ \frac{+2}{+1} = +2 $
✔ Already filled in.
---
Row 2:
- Point A: (1, 5)
- Point B: (2, 8)
- Δx = 2 - 1 =
+1
- Δy = 8 - 5 =
+3
- Gradient = $ \frac{+3}{+1} = +3 $
---
Row 3:
- Point A: (4, 5)
- Point B: (7, 11)
- Δx = 7 - 4 =
+3
- Δy = 11 - 5 =
+6
- Gradient = $ \frac{+6}{+3} = +2 $
---
Row 4:
- Point A: (3, 8)
- Point B: (-1, -4)
- Δx = -1 - 3 =
-4
- Δy = -4 - 8 =
-12
- Gradient = $ \frac{-12}{-4} = +3 $
---
Row 5:
- Point A: (-1, -6)
- Point B: (3, 10)
- Δx = 3 - (-1) = 3 + 1 =
+4
- Δy = 10 - (-6) = 10 + 6 =
+16
- Gradient = $ \frac{+16}{+4} = +4 $
---
Row 6:
- Point A: (-2, -3)
- Point B: (-4, -13)
- Δx = -4 - (-2) = -4 + 2 =
-2
- Δy = -13 - (-3) = -13 + 3 =
-10
- Gradient = $ \frac{-10}{-2} = +5 $
---
Row 7:
- Point A: (4, -5)
- Point B: (0, 3)
- Δx = 0 - 4 =
-4
- Δy = 3 - (-5) = 3 + 5 =
+8
- Gradient = $ \frac{+8}{-4} = -2 $
---
Row 8:
- Point A: (-2, -3)
- Point B: (6, -11)
- Δx = 6 - (-2) = 6 + 2 =
+8
- Δy = -11 - (-3) = -11 + 3 =
-8
- Gradient = $ \frac{-8}{+8} = -1 $
---
Row 9:
- Point A: (4, -19)
- Point B: (-2, -1)
- Δx = -2 - 4 =
-6
- Δy = -1 - (-19) = -1 + 19 =
+18
- Gradient = $ \frac{+18}{-6} = -3 $
---
Final Completed Table:
| Point A coordinates | Point B coordinates | Change in x | Change in y | Gradient |
|---------------------|---------------------|-------------|-------------|----------|
| (4, 9) | (5, 11) | +1 | +2 | +2 |
| (1, 5) | (2, 8) | +1 | +3 | +3 |
| (4, 5) | (7, 11) | +3 | +6 | +2 |
| (3, 8) | (-1, -4) | -4 | -12 | +3 |
| (-1, -6) | (3, 10) | +4 | +16 | +4 |
| (-2, -3) | (-4, -13) | -2 | -10 | +5 |
| (4, -5) | (0, 3) | -4 | +8 | -2 |
| (-2, -3) | (6, -11) | +8 | -8 | -1 |
| (4, -19) | (-2, -1) | -6 | +18 | -3 |
---
✔ All values calculated.
Summary:
The
gradient is found using the formula:
$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$
This gives us the slope of the line passing through the two points.
Let me know if you'd like the full equation of each line too!
Parent Tip: Review the logic above to help your child master the concept of finding equation of a line worksheet.
