Question

graph of following lineas equetines
$2 x - 3y = 6$
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Answer 1

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$\red{ \underline \bold{in \: the \: place \: of \: (y)wee \: can \: take(x)}} \\ \\ \orange{ \underline \bold{answer }} \\ \tt : \implies \orange{ \underline \bold{2x - 3x = 6 }} \\ \tt : \implies\orange{ \underline \bold{1x = 6 }} \\ \tt : \implies \: { \underline \bold{x = \frac{6}{1} = 6 }} \\ \\ \purple{ \underline \bold{now............. }} \\ \orange{ \underline \bold{2x - 3y = 6 }} \\ \orange{ \underline \bold{6 \: \: \: \: \: \: = \: \: \: \: \: \: 6 }} \\ \orange{ \underline \bold{lhs \: \: \:= \: \: rhs}} \\ \\ \\ \blue{ \underline \bold{i \: hope \: it \: help \: you }} \\ \\ \orange{ \underline \bold{itz \: \: shiwam............................... }}$

Answer 2

Lets reform the equation in its standard form of y=mx+c

2x+3y=6

y=−2x/3+2

Slope=−2/3,y−intercept=2

Only line with y-intercept=2 is (IV)

And it has negative slope too.

Hence, IV represents graph of 2x+3y=6.