Ratios & Proportional Relationships
GradesGrade 7Ratios & Proportional RelationshipsGraphing Proportional Relationships

Graphing Proportional Relationships

📐 Ratios & Proportional Relationships
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Graphing Proportional Relationships

A proportional relationship forms a straight line through the origin: y = kx.

Two quantities are in a proportional relationship when their ratio is always constant. On a graph, this appears as a straight line that passes through the point (0, 0) — the origin. The constant of proportionality k is the slope of that line.

y=kxwhere k=yx (constant of proportionality)y = kx \quad \text{where } k = \frac{y}{x} \text{ (constant of proportionality)}
🛒Cost of apples
Apples cost $1.50 per pound. So:
• 1 lb → $1.50
• 2 lb → $3.00
• 3 lb → $4.50

The equation is y = 1.5x. The graph is a line through (0,0) with slope 1.5.
k=yx=3.002=4.503=1.5k = \frac{y}{x} = \frac{3.00}{2} = \frac{4.50}{3} = 1.5

Proportional

Graph passes through (0, 0)y/x is constant for every pointEquation is y = kx (no added constant)

Not Proportional

Graph does NOT pass through (0, 0)y/x changes from point to pointEquation has an added constant, like y = kx + b

The origin test: if the line does not pass through (0, 0), the relationship is not proportional.

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Remember This!

To check if a table represents a proportional relationship, compute y ÷ x for each row. If all results equal the same value k, the relationship is proportional.

✏️ Try It!

A car travels at a constant speed. After 2 hours it has gone 110 miles, after 3 hours 165 miles. What is the constant of proportionality (speed)?

Practice with CalcVerse
⚖️Unit Rate & Ratio Solver📈Line Grapher (y = mx + b)
Take Quiz 📝 — 25 Questions