Linear Launch Worksheet
Linear Launch Worksheet
8th Grade Math • Rate of Change & Initial Value in Context
Name:
Date:
Period:
Model: \(y = mx + b\)
\(m\) = Rate of Change (per unit) \(b\) = Initial Value (when \(x = 0\)) Directions: Identify \(m\) and \(b\), then write the equation.
1
The GameZone arcade charges a flat $5.00 entrance card fee, plus $1.50 for each token pack purchased. Let x = token packs and y = total cost in dollars.
Rate of Change (\(m\)) value & units
Initial Value (\(b\)) starting amount
Linear Equation \(y = mx + b\)
2
A community water reservoir holds 450 gallons. To irrigate local crops, maintenance opens a valve that drains the tank at a steady rate of 25 gallons per hour. Let x = hours and y = gallons remaining.
Rate of Change (\(m\)) value & units
Initial Value (\(b\)) starting amount
Linear Equation \(y = mx + b\)
3
Elena has $60 in her savings account. She decides to save $15 each week from her neighborhood lawn mowing job. Let x = number of weeks and y = total dollars in savings.
Rate of Change (\(m\)) value & units
Initial Value (\(b\)) starting amount
Linear Equation \(y = mx + b\)
4
A hot air balloon floats at an altitude of 1,800 feet above sea level. The pilot releases warm air so the balloon descends at a steady rate of 120 feet per minute. Let x = descent minutes and y = altitude in feet.
Rate of Change (\(m\)) value & units
Initial Value (\(b\)) starting amount
Linear Equation \(y = mx + b\)
5
A screen-printing company charges a one-time artwork setup fee of $30.00 plus $8.50 per custom t-shirt printed. Let x = number of t-shirts and y = total order cost in dollars.
Rate of Change (\(m\)) value & units
Initial Value (\(b\)) starting amount
Linear Equation \(y = mx + b\)
Page 1 of 3 • Next: Tables & Graphs (Problems 6 – 10) Problems 1 – 5
Linear Launch: Tables & Graphs
Representing Linear Functions in Three Ways: Equation, Table & Graph
Name: Period:
6
A candle stands 12 inches tall when first lit. While burning, it loses height at a rate of 0.75 inches per hour. Let x = hours burned and y = candle height in inches.
Rate (\(m\)):
Initial (\(b\)):
Equation:
Data Table
Coordinate Grid (8 Intervals) \(y\)-axis label:
0
\(x\)-axis label:
7
A taco food truck charges a flat booking fee of $75.00 to travel to a party, plus $12.00 per guest for meals. Let x = number of guests and y = total catering cost in dollars.
Rate (\(m\)):
Initial (\(b\)):
Equation:
Data Table
| \(x\) (guests) | \(y\) (cost) |
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Coordinate Grid (8 Intervals) \(y\)-axis label:
0
\(x\)-axis label:
8
A ski mountain has a snow base of 54 inches on April 1st. In warm weather, the snow melts at an average rate of 2 inches per day. Let x = days after April 1st and y = snow depth in inches.
Rate (\(m\)):
Initial (\(b\)):
Equation:
Data Table
| \(x\) (days) | \(y\) (depth) |
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Coordinate Grid (8 Intervals) \(y\)-axis label:
0
\(x\)-axis label:
Page 2 of 3 • Problems 6 – 8 Continue to problems 9 & 10 on next page
Linear Launch: Graphs & Synthesis
Problems 9 – 10 • Multiple Representations Mastery
Name: Period:
9
A mobile auto detailing service charges an equipment travel fee of $25.00 plus an hourly rate of $35.00 per hour of cleaning. Let x = detailing hours and y = total customer charge in dollars.
Rate (\(m\)):
Initial (\(b\)):
Equation:
Data Table
Coordinate Grid (8 Intervals) \(y\)-axis label:
0
\(x\)-axis label:
10
A camera drone launches from a rooftop 85 feet above the street. It climbs vertically into the air at a constant rate of 18 feet per second. Let x = seconds in flight and y = drone altitude in feet.
Rate (\(m\)):
Initial (\(b\)):
Equation:
Data Table
Coordinate Grid (8 Intervals) \(y\)-axis label:
0
\(x\)-axis label:
Multiple Representations Connection: How Do They Link?
Finding Initial Value (\(b\)):
Where do you locate the initial value in a table vs. on a graph?
Finding Rate of Change (\(m\)):
How does the rate of change show up in table patterns vs. graph steepness?
Linear Functions & Modeling • CCSS 8.F.B.4 & 8.F.A.2 Page 3 of 3
