Question

Draw the graph of the equation: $2x - 3y = 5$ .
From your graph find
I.The value of y when $x = 4$
II.The value of $x$ when $y = 3$

Answer 1

Hint: In this question we have been given a linear equation and we have to draw the graph. So we will first assume any random value of $x$ , so that we get the value of $y$ . After this we have the value of both the axis and then we put the value in the graph and then draw it. We should keep in mind that the graph of a linear equation will always be a straight line.

Complete step-by-step answer:
Here we have the equation
$2x - 3y = 5$
We can also wrote the equation as
$3y = 2x - 5$
Now we will isolate the term $y$, so it gives
 $y = \dfrac{{2x - 5}}{3}$
Let us take the value of
$x = 4$ .
By substituting this in the equation, we can write
$y = \dfrac{{2(4) - 5}}{3}$
On simplifying we have
$y = \dfrac{{8 - 5}}{3}$
It gives:
$y = \dfrac{3}{3} = 1$
Now, let us take another value i.e.
 $x = - 2$
By substituting this value in the equation, we have:
$y = \dfrac{{2( - 2) - 5}}{3}$
On further solving
$y = \dfrac{{ - 4 - 5}}{3}$
It gives us
$y = \dfrac{{ - 9}}{3} = - 3$
So we can now write the values:

$x$	$4$	$ - 2$
$y$	$1$	$ - 3$

We will now put these values in the graph:

From the above graph we have the coordinates, $A(4,1)$ and $B( - 2, - 3)$ .
Based on the above graph we can also see that if we consider
$x = 4$ , then we know that the line joining the two points and a point on the Y- axis will give the value of $y$ .
Therefore we have when $x = 4$ , then the value is
$y = 1$
It gives us the same coordinate as above i.e.
$A(4,1)$
Again in the second case if we consider
$y = 3$ , then the line joining the two points and a point on the X- axis gives the value of $x$
Therefore when we have
$y = 3$ , the value on the X- axis is $x = 7$ .
Hence in the graph we have $P(7,3)$ .

Note: We should note that the standard form a linear equation is
$ax + b = 0$ . This is the example of a linear equation in one variable. If we have a linear equation in two variables, then it will be of the form $ax + by = c$ . Here $x,y$ are variables and $a,b,c$ are constants. We should know that linear equations are equations of degree $1$ .