# Consider the case when the constant a=4. plot the graph of y=4/x.

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 $a=4$.

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.

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