Question

If xy = 20, x, y > 0. Use the graph to find y when x = 5?

Answer 1

In the given question, we have been asked to find the value of y when x = 5 and the equation of a curve is given i.e. xy = 20. In order to find the value, first we need to draw the graph of the given equation by putting different values of ‘x’ and solve for the value of ‘y’. by on the graph of the equation draw a line parallel to y-axis from the point x = 5 and where it intersects the line of the given equation, from that point we will be able to find the value of ‘y’.

Complete step by step solution:
We have given that,
$\Rightarrow xy=20$
Solving the above given equation;
Put a different value of ‘x’ and solve for the value of ‘y’.
Now,
Putting x = 1
Solving for the value of ‘y’,
$\Rightarrow 1\times y=20$
Dividing both the sides of the equation by 1, we get
$\Rightarrow y=20$
Now,
Putting x = 2
Solving for the value of ‘y’,
$\Rightarrow 2\times y=20$
Dividing both the sides of the equation by 2, we get
$\Rightarrow y=10$
Therefore,
We got the points for the plotting of graph, i.e.

x	Y
1	20
2	10

Graph of the equation xy = 20 is as below;

Now,
On the graph of the above equation, from the point 5 on the x-axis draw a line parallel to y-axis. Now the line intersects the line of the graph at a point, from there draw a line parallel to x-axis.
Both the lines intersect each other at the point (5, 4) i.e. when x = 5 means x-coordinate is equal to 5, then y will be equal to 4.
Therefore,
When, x = 5 we get, y = 4.

Note:
The important thing to recollect about any equation is that the ‘equals’ sign represents a balance. What the sign says is that what’s on the left-hand side is strictly an equal to what’s on the right-hand side. It is the type of question where only mathematical operations such as addition, subtraction, multiplication and division is used.