Answer
Graph of given equation $2y + \sqrt x = 1$ is sketched as-
Work Step by Step
Given equation-
$2y + \sqrt x = 1$
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 $x = 0$ in given equation-
$2y + 0 = 1$
i.e.
$ y = \frac{1}{2} = 0.5$
Hence a point $P (0, 0.5)$ lies on the curve.
Now
Substituting $x = 1$ in given equation-
$2 y + 1 = 1$
i.e.
$ 2y = 1-1=0$
i.e.
$ y =0$
Hence the point $Q (1, 0)$ lies on the curve.
Now
Substituting $x = 4$ in given equation-
$2y + \sqrt 4 = 1$
i.e. $2 y +2 = 1$
i.e.
$ 2y = 1-2=-1$
i.e. $ y = -\frac{1}{2} = -0.5$
Hence the point $R (4, -0.5)$ lies on the curve.
Now
Substituting $x = 9$ in given equation-
$2y + \sqrt 9 = 1$
i.e. $2 y +3 = 1$
i.e.
$ 2y = 1-3=-2$
i.e. $ y = -\frac{2}{2} = -1$
Hence the point $S (9, -1)$ lies on the curve.
Now
Substituting $x = 16$ in given equation-
$2y + \sqrt 16 = 1$
i.e. $2 y +4 = 1$
i.e.
$ 2y = 1-4=-3$
i.e. $ y = -\frac{3}{2} = -1.5$
Hence the point $T (16, -1.5)$ lies on the curve.
Now we will mark the points $P, Q, R, S $ and $T$ on the graph paper and join these points AS A FREEHAND CURVE to get the graph of given equation $2y + \sqrt x = 1$
