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The graph of a proportional relationship passes through (12, 16) and (1, y). Find y.

Question:

The graph of a proportional relationship passes through {eq}(12, 16) {/eq} and {eq}(1, y) {/eq}. Find {eq}y {/eq}.

Directly Proportional :

If two variables are directly proportional and one point is known, it is possible to completely define the relationship between the two variables by introducing a constant of proportionality.

Answer and Explanation:


As the relationship between x and y is proportional, it can be written as:

{eq}y=kx {/eq}


Now having been given one point on the graph we know that y=16 when x=12. So, the value of k is found as follows.

{eq}16=12x\\ \displaystyle k=\frac 43 {/eq}


Now, the value of y when x=1 will be :

{eq}y\displaystyle =1*\frac 43\\=\displaystyle\frac 43 {/eq}


Learn more about this topic:

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Identifying the Constant of Proportionality

from 6th-8th Grade Math: Practice & Review

Chapter 50 / Lesson 13
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