Question

Is $y=3x+1$ a direct variation?

Answer 1

To find the given equation is direct variation:

Since $\left(x,y\right)=\left(0,1\right)$ is a solution to the given equation $y=3x+1$.

If the given equation is the direct variation, then for any constant $a$, so $\left(a\times 0,a\times 1\right)$ will also be a solution.

For example, take $a=3$
If it is the direct variation $\left(3\times 0,3\times 1\right)=\left(0,3\right)$ will also be a solution.

Now, substitute $x=0,y=3$ in the given equation :

$\begin{array}{rcl}3& =& 3\times 0+1\left[\text{Simplifying}\right]\\ & \Rightarrow & 3=0+1\\ \therefore 3& \ne & 1\end{array}$

Hence, the given equation $y=3x+1$ is not the direct variation.