Warm-Up 1
Day 6: Proportional Relationships and Slope
Connect proportional relationships, constant rate of change, and slope.
Student Goal
I can connect rate of change to slope.
Why It Matters
Slope helps students understand graphs, rates, linear relationships, and many real-world patterns in 8th grade and Math 1.
Warm-Up
Warm-Up 2
Which table has a constant rate of 4?
Warm-Up 3
Slope compares change in which values?
Short Lesson
Standard Focus
NC.8.EE: Expressions and Equations; NC.8.F: Functions
Student-Friendly Standard Goal
I can describe a constant rate of change and connect it to slope.
- A proportional relationship has equivalent ratios and often starts at zero.
- Rate of change tells how much y changes when x changes.
- Slope is a rate: change in y compared to change in x.
Guided Examples
Guided Example 1
Find Slope from a Table
A table has points (1, 5), (2, 9), and (3, 13). What is the slope?
| x | 1 | 2 | 3 |
| y | 5 | 9 | 13 |
Step 1
y changes +4 each time
What is the change in y from 5 to 9?
Guided Example 2
Compare Rates
Plan A costs 12 dollars for 3 hours. Plan B costs 20 dollars for 5 hours. Which has the lower hourly cost?
Step 1
12 / 3
What is Plan A's hourly cost?
Practice
Problem 1
A car travels 180 miles in 3 hours. What is the unit rate?
Problem 2
In a table, x increases by 1 and y increases by 7. What is the slope?
Problem 3
Which relationship is proportional?
Problem 4
True or false: Slope can describe speed, cost per item, or growth per week.
Problem 5
A graph rises 6 units and runs 2 units. What is the slope?
Reflection
How are you feeling about today's skill?
Optional reflection: How does slope describe a relationship?