## Proportionality:

Proportionality between variables explains the relationship between variables where the product or the ratio between the variables is equal to a constant (a proportionality constant). For example, we can say that a variable {eq}y {/eq} is proportional to {eq}x {/eq} if {eq}\dfrac{y}{x} = k\; \rm or \; xy = k {/eq}.

Robin's earnings will be proportional to the number of hours worked. Let {eq}y {/eq} be the earnings in the 9 weeks and {eq}x {/eq} be the number of hours worked in those 9 weeks. If the earning per hour is {eq}n {/eq}, then we can represent Robin's earnings as:

• {eq}y = nx {/eq}

If Robin worked 40 hours each week for the 9 weeks, then the total number of hours worked for is:

• {eq}40\times 9 = 360\; \rm hours {/eq}.

Therefore:

• {eq}y = 360n {/eq}

If Robin earned $4,320 in 9 weeks, then: • {eq}$4,320 = 360n {/eq}

Solving for n:

• {eq}n = \dfrac{ $4,320}{360} {/eq} • {eq}\boxed{\color{blue}{n = \$12\; \rm per\; hour}} {/eq}

Directly Proportional: Definition, Equation & Examples

from High School Algebra II: Help and Review

Chapter 1 / Lesson 23
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