Question

Which is the graph of the linear inequality 2x – 3y < 12? On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.

Answer 1

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Answer:

  (c)  On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.

Step-by-step explanation:

The x-coefficient is positive, so we can determine the shading from ...

  2x ... < ... (pay attention to the x-term and the inequality symbol)

That is, the solution region will have x values that are less than those on the (dashed) boundary line. Lower x-values are to the left, hence shading is on the left side of the boundary. (That's all you need to know here to make the correct choice.)

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Additional comment

If the choices are "above" or "below", then you will want to look at the y-term and the inequality symbol. If the coefficient of the variable of interest is negated (as it is for y here), then you need to consider the inequality symbol reversed: -y < ...   ⇔   y > .... Here, that means the shading is above the line. Since the slope of the line is positive, "left" and "above" are the same thing.