সমানুপাতিক

Direct Proportion

Two variables $x$ and $y$ are directly proportional if $y=kx$. Or, in words, as $x$ increases, $y$ increases as well. This is the directly proportional relationship for $k=1$:

As $x\rightarrow\infty$, $y\rightarrow\infty$ and as $x\rightarrow-\infty$, $y\rightarrow-\infty$.

(Video) Direct and Inverse Proportion

by HEGARTYMATHS

In this video, HEGARTYMATHS goes over the basics of solving problems involving direct proportionality.

If $y$ is directly proportional to $x$ we write

$$y=kx$$

In this equation, $k$ is some constant that links $y$ and $x$. When solving proportion problems, the first step is to usually solve for $k$. Once you have that, you can solve for any $x$ or $y$ value if you are given the other.

First, find $k$:

$$\begin{align} y &= kx\\\ \\ (320) &= k(80)\\ \frac{320}{80} &= k\\ \frac{4}{1} &= k\\ 4 &= k \end{align}$$

Next, plug $k$ and $y$ into the equation.

$$\begin{align} y &= kx\\\ \\ (100) &= (4)x\\ \frac{100}{4} &= x\\ 25 &= x \end{align}$$

Done!