Draw the graph of the equation `2x + 3y = 11.` From your graph, find the value of `y` when `(a) x = 7, (b) x=-8.`

Explanation

We have
`2x+3y-11 rArr y=((11-2x))/3." "` ..…(i)
Putting `x=1, " we get " y=((11-2 xx1))/3 = 9/3 =3.`
Putting `x=4," we get "y= ((11-2 xx4))/3=3/3 = 1.`
Putting `x=-2, "we get " y=({11-2 xx(-2)})/3=15/3 = 5.`
Putting `x=-5, "we get " y= ({11-2 xx ( -5)})/3=21/3 = 7.`
Thus, we have the following table: `{:(x,1,4,-2,-5),(y,3,1,5,7):}`
On a graph paper, draw lines `X'OX` and `YOY'` as the x-axis and the y-axis respectively.
On this graph paper, plot the points` A(1,3),B(4,1), C(-2,5) and D(-5,7).` Join `AB, AC and CD`, to get the straight line `BACD`. Produce it in both ways to get the required graph.

(a) On the x-axis, we take a point P for which `x=7`, i.e., `OP=7`.
From P, draw `PE bot X'OX`, meeting `DCAB` produced at `E(7,-1)`.
`:. (x=7 rArry=-1).` Thus, when `x=7`, then `y=-1`.
(b) On the x-axis, we take a point `Q` on LHS of the y-axis, such that `OQ=x=-8`.
From `Q`, draw `QF bot X'OX,` meeting BACD produced above at `F(-8,9)`.
`:. (x=-8 rArr y=9).` Thus, when `x=-8`, then `y=9`.