How do you graph the equation 2x is less than 3y plus 6?

Answer 1

First draw the equality line,

2x = 3y+6 -- (1)

or 3y = 2x-6 -- (2) to draw the line. Since the equation is about inequality, I draw the line in dashes, which means that the line marks the set boundary and no point on that line is included in the set. My dashed line crosses the axes at (3,0) and (0,-2).

Then take any point on either side of the line. I arbitrarily take (0,0), since zero makes my calculation faster. Let us work with equation (1), which is what the question asks.

Plug x=0 in the left-hand side (LHS) of equation (1); OK, zero. Plug y=0 on the right-hand side (RHS) of the equation; I get +6. I know 0 < -6, so LHS < RHS, which is exactly what the question wants. Hence, I know for sure that the region to the left of the dashed line is what I want. Shade that region (meaning drawing \\\\\ or /////) but don't go pass the drawn line. The shaded region will be the answer. BTW, 2x < 3y+6 cannot be an equation; it should be called an inequality. I suggest correcting the syntax of the question.

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