To find the slope of a line from a graph, we use the formula:
Slope = Rise / Run
-
Rise is how much the line goes up (positive) or down (negative) as you move from left to right.
-
Run is how much the line goes right (positive) or left (negative).
We pick two points on the line that are easy to read (where grid lines cross), then count the vertical change (rise) and horizontal change (run) between them.
Let’s solve each one step by step.
---
1)
Pick two points: Let’s use (-4, -2) and (0, 0).
From (-4, -2) to (0, 0):
→ Rise = 0 - (-2) = +2
→ Run = 0 - (-4) = +4
Slope = 2/4 =
1/2
✔ Check another pair: (0,0) to (4,2) → rise=2, run=4 → same result.
---
2)
Points: (0, 0) and (2, -3)
Rise = -3 - 0 = -3
Run = 2 - 0 = 2
Slope =
-3/2
Check with (-2, 3) to (0,0): rise = -3, run = 2 → same.
---
3)
Points: (0, 0) and (2, -2)
Rise = -2 - 0 = -2
Run = 2 - 0 = 2
Slope = -2/2 =
-1
Check with (-2, 2) to (0,0): rise = -2, run = 2 → same.
---
4)
Points: (0, 0) and (2, 3)
Rise = 3 - 0 = 3
Run = 2 - 0 = 2
Slope =
3/2
Check with (-2, -3) to (0,0): rise=3, run=2 → same.
---
5)
Points: (0, -3) and (1, 0)
Rise = 0 - (-3) = 3
Run = 1 - 0 = 1
Slope =
3/1 = 3
Check with (-1, -6) to (0,-3): rise=3, run=1 → same.
---
6)
Points: (0, 0) and (2, -3)
Rise = -3 - 0 = -3
Run = 2 - 0 = 2
Slope =
-3/2
Same as #2 — looks identical in steepness but mirrored? Wait — let's check direction.
Actually, from left to right: at x=-2, y=3; x=0,y=0; x=2,y=-3 → yes, same as #2.
Wait — no! In #6, when x increases, y decreases → negative slope. Same calculation.
But let me double-check coordinates.
At x=0, y=0. At x=2, y=-3 → rise=-3, run=2 → slope=-3/2
✔
---
7)
Points: (0, 0) and (4, -3)
Rise = -3 - 0 = -3
Run = 4 - 0 = 4
Slope =
-3/4
Check with (-4, 3) to (0,0): rise=-3, run=4 → same.
---
8)
Points: (0, -1) and (4, 1)
Rise = 1 - (-1) = 2
Run = 4 - 0 = 4
Slope = 2/4 =
1/2
Check with (-4, -3) to (0,-1): rise=2, run=4 → same.
---
9)
Points: (0, 0) and (2, 3)
Rise = 3 - 0 = 3
Run = 2 - 0 = 2
Slope =
3/2
Same as #4 and #5? Wait — #5 was steeper? No, #5 had rise 3 over run 1 → slope 3. This is rise 3 over run 2 → 3/2.
Check with (-2, -3) to (0,0): rise=3, run=2 → same.
Wait — actually, looking again:
In #9: from (0,0) to (2,3) → yes, rise 3, run 2 → 3/2.
But let me confirm if it passes through other points.
At x=4, y=6? Graph shows at x=4, y=6? Yes — so from (0,0) to (4,6): rise=6, run=4 → 6/4=3/2
✔
---
Now, let’s list all answers clearly:
1) 1/2
2) -3/2
3) -1
4) 3/2
5) 3
6) -3/2
7) -3/4
8) 1/2
9) 3/2
All simplified fractions or integers as required.
Final Answer:
1) 1/2
2) -3/2
3) -1
4) 3/2
5) 3
6) -3/2
7) -3/4
8) 1/2
9) 3/2
Parent Tip: Review the logic above to help your child master the concept of slope from a graph worksheet.
