What Makes A Proportional Relationship

Proportional Relationships

A proportional human relationship is one in which 2 quantities vary directly with each other. We say the variable $y$ varies directly as $x$ if:

$y=\mathrm{grand}x$

for some abiding $k$ , chosen the constant of proportionality .

(Some textbooks depict a proportional human relationship by saying that " $y$ varies proportionally with $x$ " or that " $y$ is straight proportional to $x$ .")

This means that as $x$ increases, $y$ increases and every bit $x$ decreases, $y$ decreases-and that the ratio between them always stays the aforementioned.

The graph of the proportional relationship equation is a direct line through the origin.

Example 1:

Given that $y$ varies proportionally with $x$ , with a abiding of proportionality $k=\frac{\mathrm{one}}{3}$ , find $y$ when $\mathrm{10}=12$ .

Write the equation of the proportional human relationship.

The variable $\mathrm{10}$ varies proportionally with $y$ with a constant of proportionality equal to $\frac{1}{3}$ .

So,

Substitute the given $\mathrm{ten}$ value.

Instance 2:

Given that $y$ varies proportionally with $\mathrm{ten}$ , find the constant of proportionality if $y=24$ and $x=3$ .

Write the equation of the proportional relationship.

$y=\mathrm{1000}x$

Substitute the given $x$ and $y$ values, and solve for $k$ .

$\begin{array}{l}24=m\cdot \mathrm{three}\\ k=8\end{array}$

Example 3:

Suppose $y$ varies proportionally with $\mathrm{10}$ , and $y=30$ when $\mathrm{ten}=6$ . What is the value of $y$ when $\mathrm{ten}=100$ ?

Write the equation of the proportional relationship.

$y=kx$

Substitute the given $x$ and $y$ values, and solve for $\mathrm{chiliad}$ .

$\mathrm{thirty}=m\cdot 6$

$k=5$

The equation is $y=\mathrm{v}\mathrm{ten}$ . Now substitute $\mathrm{ten}=100$ and find $y$ .

$\begin{array}{l}y=\mathrm{v}\cdot 100\\ y=500\end{array}$

What Makes A Proportional Relationship,

Source: https://www.varsitytutors.com/hotmath/hotmath_help/topics/proportional-relationships

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