Linear Equation Graphs (A) worksheet: Find the slope and y-intercept for each line.

Let's solve each of the four linear graphs by finding the slope and y-intercept for each line.

We’ll go one by one, using the standard formula:

- Slope (m) = rise / run = (change in y) / (change in x)
- Y-intercept (b) = the point where the line crosses the y-axis (x = 0)

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🔹 Graph 1 (Top Left)

Step 1: Identify two points on the line.

From the graph:
- The line passes through (-2, -4) and (4, 5)

Step 2: Calculate slope (m):
$$
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-4)}{4 - (-2)} = \frac{9}{6} = \frac{3}{2}
$$

Step 3: Find y-intercept (where x = 0).

We can use the point-slope form or just estimate from the graph.

We know it passes through (-2, -4), and slope is 3/2.

Use point-slope:
$$
y + 4 = \frac{3}{2}(x + 2)
$$
Now plug in $ x = 0 $:
$$
y + 4 = \frac{3}{2}(2) = 3 \Rightarrow y = -1
$$

So, y-intercept = -1

✔ Answer:
- Slope: $ \frac{3}{2} $
- Y-intercept: $ -1 $

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🔹 Graph 2 (Top Right)

Step 1: Identify two points.

The line passes through:
- (-8, -5)
- (8, -4)

Step 2: Calculate slope:
$$
m = \frac{-4 - (-5)}{8 - (-8)} = \frac{1}{16}
$$

Step 3: Y-intercept

Find where x = 0.

We can use the slope and a point to find it.

Using point (-8, -5):
$$
y + 5 = \frac{1}{16}(x + 8)
$$
Plug in $ x = 0 $:
$$
y + 5 = \frac{1}{16}(8) = 0.5 \Rightarrow y = -4.5 = -\frac{9}{2}
$$

Alternatively, since the line is almost flat and goes from (-8,-5) to (8,-4), at x=0, it's halfway between x=-8 and x=8, so y should be halfway between -5 and -4 → -4.5

✔ Answer:
- Slope: $ \frac{1}{16} $
- Y-intercept: $ -\frac{9}{2} $ or $ -4.5 $

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🔹 Graph 3 (Bottom Left)

Step 1: Identify two points.

Line passes through:
- (-8, -7)
- (8, 3)

Step 2: Slope
$$
m = \frac{3 - (-7)}{8 - (-8)} = \frac{10}{16} = \frac{5}{8}
$$

Step 3: Y-intercept

Use point (-8, -7) and slope $ \frac{5}{8} $

$$
y + 7 = \frac{5}{8}(x + 8)
$$
Set $ x = 0 $:
$$
y + 7 = \frac{5}{8}(8) = 5 \Rightarrow y = -2
$$

✔ Answer:
- Slope: $ \frac{5}{8} $
- Y-intercept: $ -2 $

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🔹 Graph 4 (Bottom Right)

Step 1: Identify two points.

Line passes through:
- (0, 9) ← this is the y-intercept!
- (6, 0)

Step 2: Slope
$$
m = \frac{0 - 9}{6 - 0} = \frac{-9}{6} = -\frac{3}{2}
$$

Step 3: Y-intercept

Already identified: when $ x = 0 $, $ y = 9 $

✔ Answer:
- Slope: $ -\frac{3}{2} $
- Y-intercept: $ 9 $

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✔ Final Answers:

| Graph | Slope | Y-intercept |
|-------|--------------|-------------|
| 1 | $ \frac{3}{2} $ | $ -1 $ |
| 2 | $ \frac{1}{16} $ | $ -\frac{9}{2} $ |
| 3 | $ \frac{5}{8} $ | $ -2 $ |
| 4 | $ -\frac{3}{2} $ | $ 9 $ |

Let me know if you'd like these written as equations in slope-intercept form ($ y = mx + b $)!