Graphing worksheet with four real-world scenarios represented by line graphs, asking students to find slope, y-intercept, and write equations.

Absolutely! Let’s go through each graph one by one, find the slope and y-intercept, interpret them in real-world context, and write the equation in the form y = mx + b.

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Graph 1: Pool Passes

- x-axis: Number of passes
- y-axis: Cost (dollars)

#### Step 1: Find two points on the line
Look at the graph:
- When x = 0, y = 6 → Point (0, 6)
- When x = 2, y = 12 → Point (2, 12)

#### Step 2: Calculate slope (m)
Slope = rise / run = (change in y) / (change in x)
→ m = (12 - 6) / (2 - 0) = 6 / 2 = 3

#### Step 3: y-intercept (b)
When x = 0, y = 6 → b = 6

#### Step 4: Real-world interpretation
- Slope = 3: Each additional pool pass costs $3.
- y-intercept = 6: There is a base fee of $6 even if you buy 0 passes (maybe a membership or activation fee).

#### Step 5: Equation
Let y = cost (dollars), x = number of passes
→ y = 3x + 6

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Graph 2: Number of Pizzas to Order

- x-axis: Number of people
- y-axis: Number of pizzas

#### Step 1: Pick two points
- (0, 0) — 0 people → 0 pizzas
- (10, 6) — 10 people → 6 pizzas

#### Step 2: Slope
m = (6 - 0) / (10 - 0) = 6/10 = 0.6

#### Step 3: y-intercept
At x=0, y=0 → b = 0

#### Step 4: Real-world interpretation
- Slope = 0.6: For every 1 person, you need 0.6 of a pizza (or 3/5 of a pizza). So, for every 5 people, you need 3 pizzas.
- y-intercept = 0: If there are 0 people, you order 0 pizzas — makes sense!

#### Step 5: Equation
Let y = number of pizzas, x = number of people
→ y = 0.6x

*(You could also write it as y = (3/5)x if fractions are preferred)*

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Graph 3: Cost of Birthday Cake

- x-axis: Number of servings
- y-axis: Cost (dollars)

#### Step 1: Pick two points
- (0, 0) — 0 servings → $0
- (80, 120) — 80 servings → $120? Wait — let’s check the scale.

Actually, looking closely:
- At x = 80, y = 120? But the grid goes up to 100, and the line ends at about y=120? Wait — let me recheck.

Looking again — the y-axis goes up to 100 in increments of 20. The line ends at (80, 120)? That doesn’t match the grid.

Wait — actually, the top of the graph says “Cost (dollars)” and the highest mark is 100. The line ends at x=80, y=100? Let’s confirm:

At x=0, y=0
At x=80, y=100 → that fits the grid.

So point (80, 100)

#### Step 2: Slope
m = (100 - 0) / (80 - 0) = 100/80 = 1.25

#### Step 3: y-intercept
(0,0) → b = 0

#### Step 4: Real-world interpretation
- Slope = 1.25: Each serving costs $1.25.
- y-intercept = 0: No servings means no cost — makes sense.

#### Step 5: Equation
Let y = cost (dollars), x = number of servings
→ y = 1.25x

*(Or y = (5/4)x)*

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Graph 4: Cellular Phone Plan

- x-axis: Days of month
- y-axis: Number of minutes

This line is decreasing — so slope will be negative.

#### Step 1: Pick two points
- (0, 60) — Day 0 → 60 minutes left
- (24, 0) — Day 24 → 0 minutes left

#### Step 2: Slope
m = (0 - 60) / (24 - 0) = (-60)/24 = -2.5

#### Step 3: y-intercept
At x=0, y=60 → b = 60

#### Step 4: Real-world interpretation
- Slope = -2.5: You use 2.5 minutes per day. (The negative sign means minutes are decreasing over time.)
- y-intercept = 60: On day 0 (start of the month), you have 60 minutes available.

#### Step 5: Equation
Let y = number of minutes remaining, x = days of month
→ y = -2.5x + 60

*(Or y = -(5/2)x + 60)*

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## ✔ Final Answers:

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1. Pool Passes

- Slope = 3
- y-intercept = 6
- Real-world interpretation of slope: Each additional pool pass costs $3.
- Equation: y = 3x + 6

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2. Number of Pizzas to Order

- Slope = 0.6
- y-intercept = 0
- Real-world interpretation of slope: For every person, you need 0.6 of a pizza (or 3 pizzas for every 5 people).
- Equation: y = 0.6x

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3. Cost of Birthday Cake

- Slope = 1.25
- y-intercept = 0
- Real-world interpretation of slope: Each serving costs $1.25.
- Equation: y = 1.25x

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4. Cellular Phone Plan

- Slope = -2.5
- y-intercept = 60
- Real-world interpretation of slope: You use 2.5 minutes per day.
- Equation: y = -2.5x + 60

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Let me know if you’d like these equations rewritten with fractions or in different forms!