Question

Draw the graph of the equation 2x + 3y = 12. From the graph, find the coordinates of the
point: (i) whose y-coordinates is 3. (ii) whose x-coordinate is −3.

Answer 1

Graph of the equation 2x + 3y =12 :
We have,

    ` 2x + 3y = 12 `

⇒  `2x = 12 - 3y `

⇒  ` x = (12 - 3y) /2`

Putting   y = 2 , we get  `x = (12 - 3 xx 2 )/2` = 3

Putting  y = - 4 , we get  ` x  ( 12  - 3 xx 4) / 2 = 0 ` Thus . ( 3, 0 ) and ( 0 ,4 ) are two points on the line 2x + 3y = 12

The graph of line represents by the equation  2x + 3y = 12

x	0	3
y	4	2

Graph of the equation  2x + 3y = 12

(i) To find coordinates of the points when Y = 3 we draw a line parallel to x  - axis and
passing through  ( 0,3 ) this lines meets the graph of 2X + 3Y = 12 at a point p from which
we draw a line parallel to y - axis which process x - axis at `X =3/2`
 , so the coordinates
of the required points are
 `(3/2 , 3)` .

(ii) To find the coordinates of the points when (X = - 3 ) we draw a line parallel to y-axis
and passing through (-3 , 0 ). This lines meets the graph of 2x +3y =12 at a point p
from which we draw a line parallel to x - axis crosses y - axis at y = 6, so, the
coordinates of the required point are (-3, 6) .