Answer
Graph of given equation $xy = 4$
Work Step by Step
Given equation-
$xy = 4$
To sketch graph of this equation, we can either use a graphing calculator or find some points on it to draw it as freehand curve as following-
Substituting $x = 1$ in given equation-
$1\times y = 4$
i.e.
$ y = 4$
Hence a point $P (1, 4)$ lies on the curve.
Now
Substituting $x = 4$ in given equation-
$4\times y = 4$
i.e.
$ y = 1$
Hence the point $Q (4, 1)$ lies on the curve.
Now
Substituting $x = 2$ in given equation-
$2\times y = 4$
i.e.
$ y = 2$
Hence the point $R (2, 2)$ lies on the curve.
Now
Substituting $x = 8$ in given equation-
$8\times y = 4$
i.e.
$ y = 0.5$
Hence the point $S (8, 0.5)$ lies on the curve.
Now
Substituting $x = 0.5$ in given equation-
$0.5\times y = 4$
i.e.
$ y = 8$
Hence the point $T (0.5, 8)$ lies on the curve.
Now we will mark the points $P (1,4), Q(4,1), R(2,2), S (8,0.5) $ and $T(0.5,8)$ on the graph paper and join these points AS A FREEHAND CURVE to get the graph of given equation $xy = 4$
Now as per equation, product of both the coordinates is positive, hence points with the same numerical value of $x$ and $y$ coordinates but with negative signs will also be there on the curve. Thus curve will also extends in negative direction of $x$ and $y$ axis.
i.e. points $U (-1,-4), V(-4,-1), W(-2-,2), X (-8,-0.5) $ and $Y(-0.5,-8)$ will be on the sketch in negative direction of $x$ and $y$ axis.
