The correct options are
C Perpendicular
D Coplanar
To draw the graph for the given linear equation, we need to first plot the points which lie on it, join them to get a straight line.
First equation is
2x−3y=6⟹y=23x−2Substitute different values of x in the equation and calculate to get corresponding values of y.
x
| y=23x−2
| Point (x,y)
|
0
| −2 | (0,−2)
|
3 | 0 | (3,0) |
6 | 2 | (6,2) |
−3 | −4 | (−3,−4) |
−6 | −6 | (−6,−6) |
Second equation is
x2+y3=1⟹y=−32x+3Substitute different values of x in the equation and calculate to get corresponding values of y.
x
| y=−32x+3
| Point (x,y)
|
0
| 3 | (0,3)
|
2 | 0 | (2,0) |
4 | −3 | (4,−3) |
−2 | 6 | (−2,6) |
−4 | 9 | (−4,9) |
Plot these points on the graph paper and join them using a straight line.
On observing the graph, we find that the two lines intersect each other at right angle. Hence, they are perpendicular to each other.