To find the slope of a line from a graph, we use the formula:
Slope = Rise / Run
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Rise is how much the line goes up (positive) or down (negative) between two points.
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Run is how much the line goes right (positive) or left (negative) between those same two points.
We’ll pick two clear points on each line — preferably where the line crosses grid intersections — and calculate rise over run.
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Let’s go one by one:
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Problem 1)
Line goes from (-5, 2) to (0, -3) → but let’s pick easier points: say (-4, 1) and (0, -3)
From (-4, 1) to (0, -3):
→ Down 4 units (rise = -4), Right 4 units (run = 4)
Slope = -4/4 =
-1
Check another pair: (-5, 2) to (1, -4) → down 6, right 6 → still -1 ✔️
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Problem 2)
Points: (0, -2) and (2, 2)
Up 4, right 2 → rise = 4, run = 2 → slope = 4/2 =
2
Check: (1, 0) to (3, 4) → up 4, right 2 → same ✔️
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Problem 3)
Points: (-2, -4) and (0, 2)
Up 6, right 2 → rise = 6, run = 2 → slope = 6/2 =
3
Check: (-1, -1) to (1, 5) → up 6, right 2 → same ✔️
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Problem 4)
Points: (0, -5) and (1, 0)
Up 5, right 1 → rise = 5, run = 1 → slope =
5
Check: (1, 0) to (2, 5) → up 5, right 1 → same ✔️
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Problem 5)
Points: (0, 3) and (2, 0)
Down 3, right 2 → rise = -3, run = 2 → slope =
-3/2
Check: (4, -3) to (0, 3) → down 6, right 4? Wait — better to go from (0,3) to (4,-3): down 6, right 4 → -6/4 = -3/2 ✔️
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Problem 6)
Points: (0, 0) and (4, -4)
Down 4, right 4 → rise = -4, run = 4 → slope =
-1
Check: (-2, 2) to (2, -2) → down 4, right 4 → same ✔️
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Problem 7)
Points: (0, -5) and (3, 0)
Up 5, right 3 → rise = 5, run = 3 → slope =
5/3
Check: (3, 0) to (6, 5)? Not on graph. Try (-3, -10)? Too far. Use (0,-5) and (3,0) — yes, that’s clear. ✔️
Wait — actually, looking at graph: from (0, -5) to (3, 0) is correct. But let me check if there's an integer point: (3,0) and (6,5) not shown. Alternatively, from (-3, -10) not visible. So stick with (0,-5) to (3,0). Slope = 5/3.
But wait — maybe better points: look at x= -3, y= -10? Not labeled. Actually, from (0, -5) to (3, 0) is fine.
Alternatively, from (3,0) to (0,-5): up 5, right 3 → same.
Actually, let me recheck: from (0, -5) to (3, 0): change in y = 0 - (-5) = +5; change in x = 3 - 0 = +3 → slope = 5/3 ✔️
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Problem 8)
Points: (0, -1) and (-1, 3)
From (0, -1) to (-1, 3): up 4, left 1 → rise = 4, run = -1 → slope = 4 / (-1) =
-4
Check: from (-1, 3) to (-2, 7): up 4, left 1 → same slope ✔️
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Problem 9)
Points: (0, -5) and (2, -1)
Up 4, right 2 → rise = 4, run = 2 → slope = 4/2 =
2
Check: (2, -1) to (4, 3): up 4, right 2 → same ✔️
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Now compiling all answers:
1) -1
2) 2
3) 3
4) 5
5) -3/2
6) -1
7) 5/3
8) -4
9) 2
Double-check Problem 7: Is it really 5/3? Let me see the graph again mentally.
In problem 7: Line passes through (0, -5) and (3, 0). Yes. Also, does it pass through (6,5)? Probably, but not needed. From (0,-5) to (3,0): Δy = 5, Δx = 3 → 5/3. Correct.
Problem 5: From (0,3) to (2,0): Δy = -3, Δx = 2 → -3/2. Correct.
All others seem solid.
Final Answer:
1) -1
2) 2
3) 3
4) 5
5) -3/2
6) -1
7) 5/3
8) -4
9) 2
Parent Tip: Review the logic above to help your child master the concept of slope graph worksheet.
