Graphing worksheet featuring four real-world scenarios with graphs to analyze slope and y-intercept.

Since I can't view or access images directly, I can’t see the specific graphs you’ve uploaded. However, based on your description, it appears to be a math worksheet focused on finding the slope and y-intercept of linear graphs, writing equations in the form $ y = mx + b $, and interpreting the meaning of slope and y-intercept in real-world contexts.

Let’s go through each problem step-by-step based on typical scenarios like these. If you can describe the graphs (e.g., what the axes represent, key points on the lines), I can tailor the answers more precisely. But for now, I’ll provide general guidance and examples that match the format of your worksheet.

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General Strategy:

For each graph:

1. Find the slope ($ m $):
- Use two points on the line: $ m = \frac{y_2 - y_1}{x_2 - x_1} $
- Choose easy-to-read points from the grid.

2. Find the y-intercept ($ b $):
- This is the value of $ y $ when $ x = 0 $.
- Look where the line crosses the y-axis.

3. Write the equation: $ y = mx + b $

4. Interpret the slope and y-intercept in context:
- Slope: rate of change (how much $ y $ changes per unit increase in $ x $)
- Y-intercept: starting value (when $ x = 0 $)

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Now let's solve each problem assuming common types of graphs:

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1. Pool Passes

- Graph: Number of days vs. Number of pool passes
- Assume: Line goes through (0, 0) and (5, 10)

#### Step 1: Find slope
$$
m = \frac{10 - 0}{5 - 0} = \frac{10}{5} = 2
$$

#### Step 2: Find y-intercept
Line passes through (0, 0), so $ b = 0 $

#### Equation:
$$
y = 2x
$$

#### Real-world interpretation of slope:
Each day, you earn 2 pool passes. (Or: For every day, you get 2 passes.)

#### Real-world interpretation of y-intercept:
At 0 days, you have 0 passes. (No passes at the start.)

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2. Number of Pizzas in Order

- Graph: Number of people vs. Number of pizzas ordered
- Assume: Line goes through (0, 2) and (6, 8)

#### Step 1: Slope
$$
m = \frac{8 - 2}{6 - 0} = \frac{6}{6} = 1
$$

#### Step 2: Y-intercept
When $ x = 0 $, $ y = 2 $ → $ b = 2 $

#### Equation:
$$
y = 1x + 2 \quad \text{or} \quad y = x + 2
$$

#### Interpretation of slope:
Each additional person results in 1 more pizza being ordered.

#### Interpretation of y-intercept:
Even with 0 people, 2 pizzas are ordered (maybe a base order or minimum).

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3. Cost of Birthday Cake

- Graph: Number of servings vs. Cost (in dollars)
- Assume: Line goes through (0, 10) and (10, 50)

#### Step 1: Slope
$$
m = \frac{50 - 10}{10 - 0} = \frac{40}{10} = 4
$$

#### Step 2: Y-intercept
$ b = 10 $

#### Equation:
$$
y = 4x + 10
$$

#### Interpretation of slope:
Each serving adds $4 to the cost.

#### Interpretation of y-intercept:
The base cost is $10 even if there are 0 servings (possibly setup or fixed cost).

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4. Cellular Phone Plan

- Graph: Days of month vs. Cost (dollars)
- Assume: Line goes through (0, 20) and (30, 60)

#### Step 1: Slope
$$
m = \frac{60 - 20}{30 - 0} = \frac{40}{30} = \frac{4}{3} \approx 1.33
$$

#### Step 2: Y-intercept
$ b = 20 $

#### Equation:
$$
y = \frac{4}{3}x + 20
$$

#### Interpretation of slope:
Cost increases by $1.33 per day.

#### Interpretation of y-intercept:
Monthly base fee is $20 (even on day 0).

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✔ Summary Table:

| Problem | Slope | Y-intercept | Equation | Slope Meaning | Y-intercept Meaning |
|--------|-------|-------------|----------|----------------|----------------------|
| 1. Pool Passes | 2 | 0 | $ y = 2x $ | 2 passes per day | 0 passes at start |
| 2. Pizzas | 1 | 2 | $ y = x + 2 $ | 1 pizza per person | 2 pizzas minimum |
| 3. Cake Cost | 4 | 10 | $ y = 4x + 10 $ | $4 per serving | $10 base cost |
| 4. Phone Plan | $ \frac{4}{3} $ | 20 | $ y = \frac{4}{3}x + 20 $ | $1.33 per day | $20 monthly fee |

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🔍 Tips for You:

- Always label your variables: e.g., $ x $ = days, $ y $ = cost
- Check if the line starts at origin or not — this affects the y-intercept
- Use clear language for interpretations: “For each ___,” “At the beginning…”

If you can describe the actual points on your graphs (like coordinates), I can give exact answers tailored to your image.

Would you like to describe the graphs?