Find the Slope of Each Line worksheet with eight graphs for calculating slope.

Let's solve each problem step by step to find the slope of each line. The slope of a line is calculated using the formula:

$$
\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
$$

We'll pick two points on each line from the graph and compute the slope.

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1)

Line goes from $(-4, 0)$ to $(2, 3)$

$$
\text{slope} = \frac{3 - 0}{2 - (-4)} = \frac{3}{6} = \frac{1}{2}
$$

✔ Slope = $ \frac{1}{2} $

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2)

Line goes from $(-5, -1)$ to $(4, 0)$

$$
\text{slope} = \frac{0 - (-1)}{4 - (-5)} = \frac{1}{9}
$$

✔ Slope = $ \frac{1}{9} $

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3)

Line goes from $(-1, 4)$ to $(2, -2)$

$$
\text{slope} = \frac{-2 - 4}{2 - (-1)} = \frac{-6}{3} = -2
$$

✔ Slope = $ -2 $

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4)

Line goes from $(1, 4)$ to $(1, -2)$ → Vertical line

Since $x$ doesn't change (same $x$-coordinate), the run is 0 → undefined slope

✔ Slope = undefined

> Note: Vertical lines have undefined slope.

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5)

Line goes from $(-5, 1)$ to $(3, 2)$

$$
\text{slope} = \frac{2 - 1}{3 - (-5)} = \frac{1}{8}
$$

✔ Slope = $ \frac{1}{8} $

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6)

Line goes from $(-2, -2)$ to $(2, 4)$

$$
\text{slope} = \frac{4 - (-2)}{2 - (-2)} = \frac{6}{4} = \frac{3}{2}
$$

✔ Slope = $ \frac{3}{2} $

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7)

Line goes from $(-2, -2)$ to $(2, 4)$

Wait — same as #6? Let’s double-check.

Actually, this one appears to go from $(-2, -2)$ to $(2, 4)$ — yes, same points.

But let's verify visually: it passes through origin?

Yes! From $(-2, -2)$ to $(2, 4)$:

$$
\text{slope} = \frac{4 - (-2)}{2 - (-2)} = \frac{6}{4} = \frac{3}{2}
$$

Wait — but actually, if it goes through origin $(0,0)$, then from $(0,0)$ to $(2,4)$: $\frac{4}{2} = 2$

Wait — let’s recheck coordinates.

Looking at graph 7: line goes from $(-2, -2)$ to $(2, 4)$?

From $(-2,-2)$ to $(2,4)$: rise = 6, run = 4 → slope = $ \frac{6}{4} = \frac{3}{2} $

But wait — does it pass through $(0,0)$?

Yes: $(-2,-2)$ to $(2,4)$: from $(-2,-2)$ to $(0,0)$: rise = 2, run = 2 → slope = 1

Wait — that can’t be. If from $(-2,-2)$ to $(0,0)$, slope = $ \frac{0 - (-2)}{0 - (-2)} = \frac{2}{2} = 1 $

And from $(0,0)$ to $(2,4)$: $ \frac{4}{2} = 2 $

That’s inconsistent — so not straight?

Wait — maybe I misread.

Look carefully: in graph 7, the line goes from $(-2, -2)$ to $(2, 4)$? But let’s check:

At $x = -2$, $y = -2$

At $x = 0$, $y = 0$

At $x = 2$, $y = 4$

So: from $(-2, -2)$ to $(2, 4)$:

$$
\text{slope} = \frac{4 - (-2)}{2 - (-2)} = \frac{6}{4} = \frac{3}{2}
$$

But from $(-2, -2)$ to $(0,0)$: $\frac{0 - (-2)}{0 - (-2)} = \frac{2}{2} = 1$

Contradiction — unless the point at $x=2$ is not $y=4$

Wait — look at grid: each square is 1 unit.

In graph 7: line starts at $(-2, -2)$, goes through $(0,0)$, and ends at $(2, 2)$?

Wait — no, at $x=2$, $y=4$? That would be above.

But the line seems to go from $(-2, -2)$ to $(2, 4)$ — but that would require going up 6 units over 4 units → slope $3/2$

But visually, it looks like it goes through $(1,1.5)$, etc.

But let's trust the graph.

Wait — actually, looking again: at $x=2$, $y=4$? No — the line ends at approximately $(2, 4)$? Wait, the grid goes up to $y=5$, and the line ends at $y=4$ when $x=2$?

Yes — so point $(2,4)$

And $(-2,-2)$

So:
$$
\text{slope} = \frac{4 - (-2)}{2 - (-2)} = \frac{6}{4} = \frac{3}{2}
$$

But earlier we thought it passed through origin — does it?

From $(-2,-2)$ to $(0,0)$: rise = 2, run = 2 → slope = 1

But from $(0,0)$ to $(2,4)$: rise = 4, run = 2 → slope = 2

Not consistent — so either the line isn't straight or my reading is off.

Wait — perhaps the line goes from $(-2, -2)$ to $(2, 2)$? But at $x=2$, $y=2$?

No — in graph 7, the line goes from bottom-left to top-right, passing through origin, and ends at $(2, 4)$?

Wait — no — look closely:

The line goes from $(-2, -2)$ to $(2, 2)$? At $x=2$, $y=2$? But the dot is at $y=4$?

Wait — I think I made an error.

Let me re-express:

Each graph has a grid from $-5$ to $5$ on both axes.

Let’s carefully read each point.

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Re-evaluate with accurate point reading:

#### 7)
Line passes through:
- $(-2, -2)$
- $(0, 0)$
- $(2, 2)$

Wait — at $x=2$, $y=2$? Yes — the line ends at $(2, 2)$

So from $(-2, -2)$ to $(2, 2)$:

$$
\text{slope} = \frac{2 - (-2)}{2 - (-2)} = \frac{4}{4} = 1
$$

Or from $(0,0)$ to $(2,2)$: $\frac{2}{2} = 1$

✔ Slope = $ 1 $

Earlier mistake — I thought it went to $y=4$, but no — at $x=2$, $y=2$

So correct slope is 1

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8)

Line goes from $(-4, 3)$ to $(4, -1)$

Check: at $x=-4$, $y=3$; at $x=4$, $y=-1$

$$
\text{slope} = \frac{-1 - 3}{4 - (-4)} = \frac{-4}{8} = -\frac{1}{2}
$$

✔ Slope = $ -\frac{1}{2} $

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Final Answers:

| Problem | Slope |
|--------|-------|
| 1) | $ \frac{1}{2} $ |
| 2) | $ \frac{1}{9} $ |
| 3) | $ -2 $ |
| 4) | undefined |
| 5) | $ \frac{1}{8} $ |
| 6) | $ \frac{3}{2} $ |
| 7) | $ 1 $ |
| 8) | $ -\frac{1}{2} $ |

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✔ Summary of Answers:

1) $ \frac{1}{2} $
2) $ \frac{1}{9} $
3) $ -2 $
4) undefined
5) $ \frac{1}{8} $
6) $ \frac{3}{2} $
7) $ 1 $
8) $ -\frac{1}{2} $

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Let me know if you'd like these explained with visual steps or graphs!