Proportional Function Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Determine whether yy is proportional to xx given the table: x:2,4,6x: 2, 4, 6 and y:7,14,21y: 7, 14, 21. If yes, find kk and the equation.

Solution

  1. 1
    Check ratios y/xy/x: 7/2=3.57/2=3.5; 14/4=3.514/4=3.5; 21/6=3.521/6=3.5. All equal 3.53.5.
  2. 2
    Since y/x=3.5y/x = 3.5 is constant, yy is proportional to xx with k=3.5k=3.5.
  3. 3
    Equation: y=3.5xy = 3.5x. Verify: 3.5(2)=73.5(2)=7, 3.5(4)=143.5(4)=14, 3.5(6)=213.5(6)=21. โœ“

Answer

y=3.5xy = 3.5x; k=3.5k = 3.5
To verify proportionality, check whether the ratio y/xy/x is constant across all data points. If so, the constant ratio is kk and the function is y=kxy=kx.

About Proportional Function

A proportional function has the form f(x)=kxf(x) = kx for a constant kโ‰ 0k \neq 0 โ€” it passes through the origin and the ratio f(x)/x=kf(x)/x = k is constant.

Learn more about Proportional Function โ†’

More Proportional Function Examples

Example 1 easy

The weight of water is proportional to its volume. [formula] liters weighs [formula] kg. Write the f

Example 3 easy

Hooke's Law states spring force is proportional to stretch: [formula]. If [formula] N when [formula]

Example 4 medium

Explain why [formula] is NOT a proportional function, and find the value of [formula] that would mak

โ† All Proportional Function Examples Proportional Function Concept