Every Friday the Taco Truck parks outside Mia's school. Each taco costs $2.50 — no matter how many you buy.
Mia wants to figure out the total cost for any number of tacos without doing mental math at the window. She builds a table:
The Taco Truck Problem
Story
| Tacos (x) | Cost (y) | y ÷ x |
|---|---|---|
| 1 | $2.50 | 2.50 |
| 2 | $5.00 | 2.50 |
| 5 | $12.50 | 2.50 |
| 10 | $25.00 | 2.50 |
She notices y ÷ x is always 2.50. That constant ratio means tacos and cost are proportional — and 2.50 is the constant of proportionality (also called the unit rate).
Rate Explorer
Interactive
Drag the sliders to see the table, graph, and equation all update together.
y = 2.50 × x
| x (tacos) | y (cost) | y ÷ x |
|---|
Every row gives the same y ÷ x. That's k.
Proportional graph = straight line through (0, 0)
Finding k — Step by Step
Math
Given any table or graph, here's how to find the constant of proportionality k and write the equation.
1
Pick any row in the table and divide
k = y ÷ x → $12.50 ÷ 5 = $2.50
2
Verify — every row must give the same k
$5.00 ÷ 2 = $2.50 ✓ $25.00 ÷ 10 = $2.50 ✓
3
Write the equation using y = kx
y = 2.50x (cost = $2.50 times the number of tacos)
4
Read the graph: find the point (1, k)
Point (1, 2.50) → when x = 1, y = k. The slope of the line equals k.
Key graph facts: (0, 0) is always on a proportional line (zero tacos = zero cost). (1, k) gives the unit rate directly — it's the point where x = 1.
Is It Proportional?
Practice
For each table, check whether y ÷ x stays the same in every row. Which table shows a proportional relationship?
Table A
| x | 2 | 4 | 6 | 8 |
| y | 6 | 12 | 18 | 24 |
| y÷x | 3 | 3 | 3 | 3 |
Table B
| x | 2 | 4 | 6 | 8 |
| y | 7 | 11 | 15 | 19 |
| y÷x | 3.5 | 2.75 | 2.5 | 2.375 |
Unit Rates Everywhere
Connect
A unit rate is a ratio where the second quantity is 1. It's always the k in y = kx, and it appears everywhere in daily life:
🚗 60 mphMiles per 1 hour — speed is a unit rate: d = 60t
💧 $1.29/galCost per 1 gallon — price: cost = 1.29 × gallons
🫀 70 bpmBeats per 1 minute — heart rate: beats = 70t
🌍 1 cm = 50 kmMap scale — distance = 50 × cm on map
Whenever you see "per", "each", or "every 1 ___" you're looking at a unit rate — and it's the k in y = kx.
Why it matters — Khan Academy 7.RP standards
This lesson covers CCSS 7.RP.A.1–2 from Khan Academy's 7th-grade unit. Proportional reasoning is the bridge between arithmetic and algebra: once you own y = kx, you can solve unit rates (7.RP.A.1), test tables and graphs for proportionality (7.RP.A.2a–b), write equations (7.RP.A.2c), and interpret graph points like (0,0) and (1,k) (7.RP.A.2d). These ideas power everything from cooking recipes and currency exchange to science experiments and map reading.