Question

How do you determine whether each question is a linear equation: $5x=y-4$?

Answer 1

Hint: The given equation of $5x=y-4$ is an equation of line. We convert the equation into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$ to find the intercepts and plot the line on the graph. We get the graphical form of the linear equation.

Complete step-by-step solution:
We try to draw the equation on a graph to find the line.
We have to find the x-intercept, and y-intercept of the line $5x=y-4$.
For this we convert the given equation into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$. From the form we get that the x intercept, and y intercept of the line will be $p$ and $q$ respectively. The points will be $\left( p,0 \right),\left( 0,q \right)$.
The given equation is $5x=y-4$. Converting into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$, we get
$\begin{align}
  & 5x=y-4 \\
 & \Rightarrow 5x-y=-4 \\
 & \Rightarrow \dfrac{x}{{}^{-4}/{}_{5}}+\dfrac{y}{4}=1 \\
\end{align}$
Therefore, the x intercept, and y intercept of the line $5x=y-4$ is $\dfrac{-4}{5}$ and 4 respectively. The axes intersecting points are \[\left( \dfrac{-4}{5},0 \right),\left( 0,4 \right)\].

Note: We can also use the concept of indices value for the variables. We have two variables of x and y. Both of them have the highest indices’ value of 1. This value represents the linear equation. But we need to remember that in case of \[xy+x+y=0\], the indices value becomes 2 as there are multiplication of two variables.