Practice worksheet for finding the slope of a line from a graph.

I will solve this worksheet by calculating the slope for each of the nine graphs. The slope (m) is calculated using the formula: `m = (change in y) / (change in x)` or `m = (y2 - y1) / (x2 - x1)`. I'll go through each graph one by one.

First Row

Graph 1 (Top Left):
- This line goes from left to right, sloping downwards.
- I can pick two points: let's say (-4, 2) and (4, 0).
- Change in y = 0 - 2 = -2
- Change in x = 4 - (-4) = 8
- Slope (m) = -2 / 8 = -1/4

Graph 2 (Top Middle):
- This line goes from bottom left to top right, sloping upwards.
- Points: (-2, -2) and (2, 2)
- Change in y = 2 - (-2) = 4
- Change in x = 2 - (-2) = 4
- Slope (m) = 4 / 4 = 1

Graph 3 (Top Right):
- This line also slopes upwards.
- Points: (-2, -1) and (2, 3)
- Change in y = 3 - (-1) = 4
- Change in x = 2 - (-2) = 4
- Slope (m) = 4 / 4 = 1

Second Row

Graph 4 (Middle Left):
- This line slopes steeply downwards.
- Points: (-1, 4) and (1, -2)
- Change in y = -2 - 4 = -6
- Change in x = 1 - (-1) = 2
- Slope (m) = -6 / 2 = -3

Graph 5 (Middle Middle):
- This line slopes gently upwards.
- Points: (-4, -1) and (4, 1)
- Change in y = 1 - (-1) = 2
- Change in x = 4 - (-4) = 8
- Slope (m) = 2 / 8 = 1/4

Graph 6 (Middle Right):
- This is a horizontal line.
- For any two points on a horizontal line, the change in y is 0.
- Points: (-2, 2) and (2, 2)
- Change in y = 2 - 2 = 0
- Change in x = 2 - (-2) = 4
- Slope (m) = 0 / 4 = 0

Third Row

Graph 7 (Bottom Left):
- This line slopes downwards.
- Points: (-4, 2) and (0, -2)
- Change in y = -2 - 2 = -4
- Change in x = 0 - (-4) = 4
- Slope (m) = -4 / 4 = -1

Graph 8 (Bottom Middle):
- This line slopes steeply downwards.
- Points: (-1, 4) and (1, -4)
- Change in y = -4 - 4 = -8
- Change in x = 1 - (-1) = 2
- Slope (m) = -8 / 2 = -4

Graph 9 (Bottom Right):
- This line slopes steeply upwards.
- Points: (-2, -2) and (2, 6)
- Change in y = 6 - (-2) = 8
- Change in x = 2 - (-2) = 4
- Slope (m) = 8 / 4 = 2

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Final Answers:

Here are the slopes for each graph:

First Row:
- Graph 1: $ m = -\frac{1}{4} $
- Graph 2: $ m = 1 $
- Graph 3: $ m = 1 $

Second Row:
- Graph 4: $ m = -3 $
- Graph 5: $ m = \frac{1}{4} $
- Graph 6: $ m = 0 $

Third Row:
- Graph 7: $ m = -1 $
- Graph 8: $ m = -4 $
- Graph 9: $ m = 2 $

This completes the worksheet. Each slope was calculated by selecting two clear points on the line and applying the slope formula.