Question

plot the graph of the following linear equation 2(X+3-(3y+1) =0.​

Answer 1

$2(x + 3y) - 3(y + 1) = 0$

$2x + 6 - 3y - 3 = 0$

$2x - 3y + 3 = 0....(i)$

put values of x and y given as follow in eq (i)

$\fcolorbox{pink}{pink}{x}\boxed{ - 1.5} \boxed{0} \boxed{3} \\ \fcolorbox{pink}{pink}{y} \boxed{0} \boxed{1} \boxed{3}$

(graph is in ATTACHMENT)

Answer 2

the equation given is,

$2(x + 3) - 3(y + 1) = 0 \\ = 2x + 6 - 3y + 3 = 0 \\ 2x - 3y + 3 = 0$

$= 2x + 3 = 3y$

$= y = \frac{2x + 3}{3}$

$when \: x = 0 | y = 1 \\ when \: x = - 1.5 | y = 0 \\ when \: x = 3 | y = 3$

☞︎︎︎the line segment intercepted between the axes lies in the second quadrant.

☞︎︎︎the region between line and the coordinate axes is shaded as shown in the above figure.

☞︎︎︎the triangle formed is AOB.The coordinates of the vertices are A(0,1);O(0,0);B(-1.5,0)