In a mathematical equation, the linear equation has the highest degree of 1, which is why it is called a** linear equation**. A **linear equation** can be represented in both a **1** variable and **2** variable form. Graphically, a linear equation is shown by a straight line on the **x-y** coordinate system.

**A linear equation is comprised of two elements, namely constants and variables.** In one variable, the standard linear equation is represented as

\[ax+b=0, \ where \ a ≠ 0 \ and \ x \ is \ the \ variable.\]

With two variables, the standard linear equation is represented as

\[ax+by+c=0, \ where \ a ≠ 0, \ b ≠ 0 \ and \ x \ and \ y \ are \ the \ variable.\]

In this question, we have to plot the graph, whose equation is given to us as $y= \dfrac{4}{x} $. Here, the value is given as $a=4$.

## Expert Answer

The standard form of the linear equation in $2$ variables is represented as $Px+Qy=R$. In the linear form of an equation, we can easily find both $x-intercept$ and $y-intercept$, especially when dealing with systems of two linear equations. For example, $61x+45y=34$ is a linear equation.

To graph the given equation in question we have to find the respective $x$ and $y$ coordinates.

For this, we have the equation:

\[ y= \dfrac{4} {x} \]

where $a=4$

First putting the value of $x=1$, we get:

\[ y= \dfrac {4}{1} \]

\[ y =4 \]

we get the coordinates $(1,4)$

Now putting the value of $x=2$, we get:

\[ y = \dfrac {4}{2} \]

\[ y=2 \]

we get the coordinates $(2,2)$

Putting the value of $x=3$, we get:

\[ y= \frac {4}{3} \]

\[ y=1.33 \]

we get the coordinates $(3 , \dfrac {4}{3} )$

Putting the value of $ x= 4 $, we get:

\[ y= \frac {4}{4 } \]

\[ y=1 \]

we get the coordinates $(4,1)$

So our required coordinates are $ ( 1 , 4 ) , ( 2 , 2) , ( 3 , \dfrac { 4 } { 3 } ) , ( 4 , 1 ) $, now plotting these coordinates on graph we get the following graph:

Figure 1

## Numerical Results

The required coordinates for plotting the graph of equation $ y = \dfrac { 4 } { x } $ are $ D = ( 1 , 4 ) , E = ( 2 , 2) , F = ( 3 , \dfrac { 4 } { 3 } ) , G =( 4 , 1 ) $ as shown in the above graph.

## Example

Plot the graph for the equation $y=2x+1$

Solution: First we will find its respective y-coordinates by putting values of $x$

when $x=-1$

\[y=2(-1)+1=-1\]

when $x=0$

\[y=2(0)+1=1\]

when $x=1$

\[y=2(1)+1=-3\]

when $x=2$

\[y=2(2)+1=5\]

So our required coordinates are $(-1 ,-1), (0,1), (1,3), (2,5)$, now plotting these coordinates on graph we get the following graph

Figure 2

*Image/Mathematical drawings are created in Geogebra.*