Math worksheet for calculating slope from graphs, featuring six problems with instructions to draw various shapes.

Let’s solve each problem step by step. We’re finding the slope, labeled as “m”, for each line shown on the coordinate grid.

Slope (m) = rise / run
That means: how much the line goes up or down (rise) divided by how much it goes left or right (run).

We’ll pick two clear points on each line and calculate.

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Problem 7:

Line passes through (0, 0) and (5, 4).
Rise = 4 - 0 = 4
Run = 5 - 0 = 5
→ m = 4/5

Check another pair: (-5, -4) to (0, 0) → same result: rise=4, run=5 → m=4/5 ✔

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Problem 8:

Line passes through (0, -3) and (2, 1).
Rise = 1 - (-3) = 4
Run = 2 - 0 = 2
→ m = 4/2 = 2

Check with (1, -1) to (3, 3): rise=4, run=2 → m=2 ✔

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Problem 9:

Line passes through (3, 0) and (5, 5).
Rise = 5 - 0 = 5
Run = 5 - 3 = 2
→ m = 5/2

Check with (1, -5) to (3, 0): rise=5, run=2 → m=5/2 ✔

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Problem 10:

Line is almost vertical. Passes through (-2, -5) and (-2, 5)? Wait — no, looking closely:

Actually, from graph: point at (-2, -5) and (-2, 5)? That would be undefined slope — but let’s check coordinates.

Wait — actually, looking again: the line goes from approximately (-2.2, -5) to (-2, 5)? No — better to use exact grid points.

Actually, from the graph: one point is (-2, -5), another is (-2, 5)? But that’s a vertical line — which has undefined slope.

But wait — look again: the line is not perfectly vertical? Let me recheck.

Actually, in Problem 10, the line goes from about x=-2.1 to x=-2.0? Hmm — perhaps it's meant to be vertical?

Wait — let’s read the graph carefully.

Point A: (-2, -5)
Point B: (-2, 5) — yes, same x-value → vertical line → slope is undefined

But sometimes worksheets expect you to say "undefined" or write "no slope".

However, looking at the other problems, they all have numerical answers. Maybe I misread.

Wait — let’s look again at Problem 10 graph.

Actually, the line goes from (-2, -5) to (-1.8, 5)? No — that doesn’t make sense.

Perhaps it’s from (-2, -5) to (-2, 5) — definitely vertical.

But let’s check the direction: Directions say “Draw a callout box” — maybe irrelevant.

Alternatively, maybe the line is from (-2, -5) to (-1.9, 5)? Still nearly vertical.

Wait — perhaps I should use two integer points.

Looking again: The line appears to go through (-2, -5) and (-2, 5) — so Δx = 0 → division by zero → undefined.

But since this is likely expecting a number, maybe I made a mistake.

Wait — let’s try different points.

What if we take (-2, -5) and (-1.5, 0)? Then:

Rise = 0 - (-5) = 5
Run = -1.5 - (-2) = 0.5
→ m = 5 / 0.5 = 10

Is that accurate? From (-2, -5) to (-1.5, 0): yes, that seems to lie on the line.

From (-1.5, 0) to (-1, 5): rise=5, run=0.5 → m=10

Yes! So the line is very steep but not vertical. It goes up 5 units for every 0.5 units right → slope = 10.

So m = 10

✔ Confirmed.

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Problem 11:

Vertical line at x = 2. Goes from (2, -5) to (2, 5).
Δx = 0 → slope is undefined

But again, maybe they want us to recognize it’s vertical.

In math, vertical lines have no defined slope.

But let’s see the pattern — previous ones had numbers.

Wait — perhaps I misread the graph.

Looking again: Problem 11 shows a vertical line at x=2. Yes.

So slope is undefined.

But maybe in context of worksheet, they accept “undefined” or leave blank? But instruction says “m = ___”

Hmm.

Wait — perhaps it’s not vertical? Let me double-check.

No — it’s clearly drawn straight up and down at x=2.

So technically, slope is undefined.

But let’s hold that thought and check Problem 12 first.

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Problem 12:

Horizontal line at y = -2. From (-5, -2) to (5, -2).
Rise = 0
Run = any non-zero → m = 0 / run = 0

So m = 0 ✔

Now back to Problem 11.

If Problem 12 is horizontal → m=0, then Problem 11 vertical → m=undefined.

But perhaps the worksheet expects “undefined” written out.

Since the user didn’t specify format, and given that in many school contexts, vertical line slope is called “undefined”, we’ll go with that.

But let’s confirm all:

Summary:

7. m = 4/5
8. m = 2
9. m = 5/2
10. m = 10
11. m = undefined
12. m = 0

Wait — for Problem 10, earlier I said m=10 based on points (-2,-5) and (-1.5,0). Is that correct?

Let me verify with another pair.

Take (-2, -5) and (-1, 5):
Rise = 5 - (-5) = 10
Run = -1 - (-2) = 1
→ m = 10/1 = 10 ✔

Perfect.

For Problem 11: vertical line → no slope → undefined.

Some systems write “DNE” or “not defined”, but “undefined” is standard.

Now, for final answer, since the question asks for “m = ___” for each, we list them.

Final Answer:

7. m = 4/5
8. m = 2
9. m = 5/2
10. m = 10
11. m = undefined
12. m = 0

But let’s write them neatly.

Note: For fractions, we can leave as improper or mixed? 5/2 is fine.

Also, for Problem 7, 4/5 is already simplified.

All good.

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Final Answer:
7. m = 4/5
8. m = 2
9. m = 5/2
10. m = 10
11. m = undefined
12. m = 0