Math worksheet for calculating slope from graphs.

Let’s solve each problem step by step.

We are finding the slope of each line using the formula:

> Slope = rise / run

Where:
- Rise is how much the line goes up (or down) vertically between two points.
- Run is how much the line goes right (or left) horizontally between those same two points.

If the line goes up, rise is positive. If it goes down, rise is negative.
If the line goes right, run is positive. If it goes left, run is negative.

We’ll pick two clear points on each line (preferably where they cross grid lines) and calculate.

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Problem 1)

Points: Let’s use (-3, 2) and (-1, -2)

From (-3, 2) to (-1, -2):

- Rise: from y=2 to y=-2 → that’s down 4 → rise = -4
- Run: from x=-3 to x=-1 → that’s right 2 → run = +2

Slope = -4 / 2 = -2

✔ Check: From (-1, -2) to (0, -4): down 2, right 1 → slope = -2/1 = -2 → matches.

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Problem 2)

Points: Use (-3, 1) and (1, 4)

From (-3, 1) to (1, 4):

- Rise: 4 - 1 = +3
- Run: 1 - (-3) = +4

Slope = 3/4

✔ Check: From (1,4) to (5,7)? Wait — let’s check another pair. Actually, from (-3,1) to (1,4) is correct. Also, from (1,4) to (5,7) would be rise 3, run 4 → same. But wait — looking at graph, point at (1,4) and (-3,1) — yes, that’s accurate.

Wait — actually, let me double-check coordinates.

Looking again: At x = -3, y = 1 → point A(-3,1)
At x = 1, y = 4 → point B(1,4)

Yes. So rise = 3, run = 4 → slope = 3/4

But wait — is there a better pair? What about (0, 3.25?) No — better to stick with integer points.

Actually, let’s try from (-3,1) to (1,4): yes, that’s fine.

Alternatively, from (-3,1) to (5,7)? That would be rise 6, run 8 → still 3/4.

So slope = 3/4

Wait — hold on! Looking at the graph again — when x=0, y seems to be around 3.25? But we don’t need that. We have two exact points: (-3,1) and (1,4). Both are on grid intersections? Let me confirm:

In problem 2: The line passes through (-3,1) and (1,4). Yes — both are clearly marked dots.

So slope = (4 - 1)/(1 - (-3)) = 3/4 → 3/4

✔ Confirmed.

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Problem 3)

Points: Use (-4, 2) and (4, 0)

From (-4, 2) to (4, 0):

- Rise: 0 - 2 = -2
- Run: 4 - (-4) = +8

Slope = -2 / 8 = -1/4

✔ Check: From (-4,2) to (0,1): down 1, right 4 → slope = -1/4 → matches.

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Problem 4)

Points: Use (-4, -4) and (1, 1)

From (-4, -4) to (1, 1):

- Rise: 1 - (-4) = +5
- Run: 1 - (-4) = +5

Slope = 5/5 = 1

✔ Check: From (0,0) to (1,1) → rise 1, run 1 → slope 1 → matches.

Also, the line goes through origin — so slope should be 1 if it’s diagonal like that.

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Problem 5)

This is a horizontal line.

Points: Use (-3, -3) and (1, -3)

From (-3, -3) to (1, -3):

- Rise: -3 - (-3) = 0
- Run: 1 - (-3) = +4

Slope = 0 / 4 = 0

✔ Horizontal lines always have slope 0.

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Problem 6)

Points: Use (-4, -3) and (-2, 3)

From (-4, -3) to (-2, 3):

- Rise: 3 - (-3) = +6
- Run: -2 - (-4) = +2

Slope = 6 / 2 = 3

✔ Check: From (-2,3) to (-1,6)? Not shown, but from (-4,-3) to (-3,0): up 3, right 1 → slope 3 → matches.

Another check: from (-3,0) to (-2,3): up 3, right 1 → slope 3 → perfect.

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Now, compiling all answers:

Final Answer:
1) -2
2) 3/4
3) -1/4
4) 1
5) 0
6) 3