Question

Draw the graph of the equation 3x -4y =12. From the graph check whether x=4 and y=2 is its solution or not.

Answer 1

Hint: We know that equation 3x – 4y =12 is the equation of two variables. So, to plot its graph first we will find minimum three points which satisfies it and then plot those point on the graph and then join all those points to get your required line (i.e. 3x – 4y = 12). Now, to see whether x=4 and y=2 is the solution of line 3x-4y=12 or not, we will plot point (4,2) also on the same graph and then check whether the point lies on the line or not and if the point lies on the line it means that it is its solution of equation 3x-4y=12 otherwise not.

Complete step by step answer:
From the question, we can see that 3x-4y =12 is an equation of two variables x and y. So, to find different points that lies on that line we have to assume anyone variable with some constant and then we will find the value of another variable.
At first, we will find different values of x by assuming the different values of y.
Let us assume that y=0.
Now, put y=0, in equation 3x – 4y =12 to find x.
$\Rightarrow 3x-4\left( 0 \right)=12$
$\Rightarrow 3x=12$
$\therefore x=4$
Now, let us assume that y=3.
Now, put y=3 in the equation 3x – 4y =12 to find x.
$\Rightarrow 3x-4\left( 3 \right)=12$
$\Rightarrow 3x=24$
$\therefore x=8$
Now, let us assume that y=-3
$\Rightarrow 3x-4\left( -3 \right)=12$
$\Rightarrow 3x=0$
$\therefore x=0$

Now,

x	4	8	0
y	0	3	-3

Now, we will plot all the above points on the graph and join these points using a single line, then we will get our required graph.

This is our required graph of the equation 3x-4y=12.
Now, we have to check whether x=4 and y=2 is the solution of the above line 3x-4y=12 or not.
It means indirectly that we have to check whether a point (4,2) lies on the above-plotted line or not.
So, now we will plot the point (4,2) on the same above graph.

From the graph, we can see that point (4, 2) lies above the line 3x-4y=12.and not on the line we have plotted.
Hence, we can say that x=4 and y=2 are not solutions to the above graph.

Note: There is also an alternative method to check whether any point is the solution of the given equation or not. So, to check whether x=4 and y=2 is the solution of the equation 3x-4y=12 or not we can directly replacing x by 4 and y by 2 from the left-hand side of the equation and solve it and if the value we get is equal to the right-hand side of the equation then we will say that x=4 and y=2 is its solution otherwise not.