Road Trip Equation Graphic Organizer
Road Trip Equation
Part 1: Problem Breakdown & Equation Formulation
Name:
Date:
Period:
Scenario Prompt
Jamison is planning a road trip and wants to calculate the total distance he will travel. He writes a linear equation to represent the relationship between the number of days of his trip (\(x\)) and the total distance he will travel (\(y\)). He knows he should travel about 300 miles per day on average.
1
Identify Variables & Rate of Change
Input (\(x\))
What does \(x\) represent?
Unit: __________________
Output (\(y\))
What does \(y\) represent?
Unit: __________________
Rate of Change (\(m\))
Miles driven per 1 day:
Unit: miles / day
2
Build the Function Table
Complete the pattern:
| Days (\(x\)) | Calculation / Pattern | Total Miles (\(y\)) |
|---|
| 0 | 300 × 0 | 0 |
| 1 | 300 × 1 | 300 |
| 2 | 300 × 2 | |
| 3 | 300 × 3 | |
| \(x\) | 300 × \(x\) | \(y\) |
Constant Rate
For every 1 day added, the total distance increases by 300 miles.
Rate of Change (Slope, \(m\)) \(m = \frac{\text{Change in } y}{\text{Change in } x} = \frac{300}{1} = 300\)
Since he hasn't traveled any miles at Day 0, the starting amount (y-intercept, \(b\)) is \(0\).
3
Write the Equation
Target Question 1: What would his equation be? Form: \(y = mx + b\)
\(y =\)
\(y\) = total distance traveled (miles)
\(x\) = number of days on the road
Road Trip Linear Modeling • Page 1 of 2 Continue to Page 2 for Calculations & Graphing
Road Trip Equation
Part 2: Evaluation, Graphing & Application
Student Name:
4
Target Question 2: How far would he travel in 7 days?
Show Your Work (Step-by-Step)
Substitute \(x = 7\) into your linear equation:
Final Answer
Value of \(y\) when \(x = 7\):
Remember to label your units!
5
Graph the Linear Relationship
0 300 600 900 1200 1500 1800 2100 1 2 3 4 5 6 7 Time (Days, \(x\)) Distance (Miles, \(y\))
Plotting Checklist
- Plot the origin \((0, 0)\).
- Plot day 1: \((1, 300)\).
- Plot day 7: \((7, \text{___})\).
- Use a straightedge to connect points with a line starting at the origin.
6
Summary Sentence & Road Trip Detour
Contextual Summary
Write your complete answer in context:
Road Trip Detour! (Extension)
What if Jamison had already driven 50 miles before Day 1 officially began?
New Equation: \(y =\)
Road Trip Linear Modeling • Page 2 of 2 Final Check: Equation formulated • Solution computed with units • Graph verified
