Question

Draw the graph of the equation 3x – 4y = 12 and use the graph drawn to find the value of \[{y_1}\], when x = 4.

Answer 1

Hint:- To draw a graph of the given linear equation we had to find any two points that lie on that line. So, we first put x = 0 in the given equation and find the first point and then put y = 0 and find the other points that line on the given equation. And after joining two points we will get the required graph of the given equation.

Complete Step-by-Step solution:
As we know that all the points lying on the y-axis of the coordinate plane have their x-coordinate equal to zero.
And all the points lying on the x-axis of the coordinate plane have their y-coordinate equal to zero.
So, let's find the points where the equation 3x – 4y = 12 intersects the x-axis and the y-axis.
So, put y = 0 in the given equation. We get,
3x – 0 = 12
Dividing both sides of the above equation by 3. We get,
x = 4
So, the given equation cut the x-axis at the point A(4, 0)
Now, put x = 0 in the given equation. We get,
0 – 4y = 12
Dividing both sides of the above equation by –4. We get,
y = – 3
So, the given equation cut the y-axis at the point B(0, – 3)
So, now let us draw the line joining points A(4, 0) and B(0, – 3).

Now according to the question, we had to find the value of \[{y_1}\], when x = 4. So, we check from the above graph that what is the y-coordinate of a point whose x-coordinate is equal to 4 and the point lies on the given equation.
Now as we can clearly see from the above graph that the point A(4, 0) lies on the given equation and its x-coordinate is equal to 4.
So, the value of \[{y_1}\] will be 0 when x = 4.
Hence, \[{y_1}\]= 0
Note:- Whenever we come up with this type of problem then we should remember that all the points on the x-axis have their y-coordinate equal to zero and all the points on the y-axis have their x-coordinate equal to zero. And if we are asked to plot a linear equation in the graph then we need at least two points which lie on that equation. So, the easiest way to find the two points will be by putting values of x and y in the given equation equal to zero one by one and then finding the corresponding value of y and x. And then line joining these two points will be the graph of the given equation. After that, to find the value of \[{y_1}\] for the given value of x = 4, we check the point whose x-coordinate is equal to 4 and which lies on the given equation. The y-coordinate of that point will be the required value of \[{y_1}\].