Interpreting-slope-and-y-intercept-worksheet - Free Printable

Let’s solve each graph one by one. We’ll find the slope, y-intercept, interpret what they mean in real life, and write the equation for each.

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Problem 1: Pool Passes

Graph shows:
- x-axis: Number of passes (0 to 10)
- y-axis: Cost in dollars (0 to 30)

The line starts at (0, 6) → that’s the y-intercept.
It goes through (2, 12), (4, 18), etc.

Slope = rise over run = change in y / change in x

From (0,6) to (2,12):
rise = 12 - 6 = 6
run = 2 - 0 = 2
slope = 6/2 = 3

Y-intercept = 6 (where the line crosses the y-axis when x=0)

Real-world interpretation of slope:
Each additional pool pass costs $3.

Equation:
y = mx + b → y = 3x + 6
But let’s use meaningful variables:
Let C = cost in dollars, P = number of passes
→ C = 3P + 6

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Problem 2: Number of Pizzas to Order

Graph shows:
- x-axis: Number of people (0 to 10)
- y-axis: Number of pizzas (0 to 10)

Line starts at (0,0) → y-intercept = 0
Goes through (2,1), (4,2), (6,3), (8,4), (10,5)

Slope = rise/run = from (0,0) to (2,1):
rise = 1, run = 2 → slope = 1/2 = 0.5

Y-intercept = 0

Real-world interpretation of slope:
For every 2 people, you need 1 pizza → or, each person gets half a pizza on average.

Equation:
Let N = number of pizzas, P = number of people
→ N = 0.5P

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Problem 3: Cost of Birthday Cake

Graph shows:
- x-axis: Number of servings (0 to 80)
- y-axis: Cost in dollars (0 to 100)

Line starts at (0,0) → y-intercept = 0
Goes through (16,20), (32,40), (48,60), (64,80), (80,100)

Slope = rise/run = from (0,0) to (16,20):
rise = 20, run = 16 → slope = 20/16 = 5/4 = 1.25

Y-intercept = 0

Real-world interpretation of slope:
Each serving costs $1.25.

Equation:
Let C = cost in dollars, S = number of servings
→ C = 1.25S

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Problem 4: Cellular Phone Plan

Graph shows:
- x-axis: Days of month (0 to 24)
- y-axis: Number of minutes (0 to 100)

Line starts at (0,60) → y-intercept = 60
Ends at (24,0)

Slope = rise/run = from (0,60) to (24,0):
rise = 0 - 60 = -60
run = 24 - 0 = 24
slope = -60/24 = -2.5 → -2.5

Y-intercept = 60

Real-world interpretation of slope:
You lose 2.5 minutes per day — meaning your plan gives you 60 minutes total, and you use them up at a rate of 2.5 minutes per day.

Equation:
Let M = minutes left, D = days into the month
→ M = -2.5D + 60

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Final Answer:

1. Pool Passes
Slope = 3
y-intercept = 6
Real-world interpretation of slope: Each pool pass costs $3.
Equation: C = 3P + 6

2. Number of Pizzas to Order
Slope = 0.5
y-intercept = 0
Real-world interpretation of slope: For every 2 people, order 1 pizza (or 0.5 pizza per person).
Equation: N = 0.5P

3. Cost of Birthday Cake
Slope = 1.25
y-intercept = 0
Real-world interpretation of slope: Each serving costs $1.25.
Equation: C = 1.25S

4. Cellular Phone Plan
Slope = -2.5
y-intercept = 60
Real-world interpretation of slope: You use 2.5 minutes per day from your monthly allowance.
Equation: M = -2.5D + 60