How do you graph the inequality $2 x + 3 y > 6$ $2x + 3y > 6$ ?

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How do you graph the inequality $2 x + 3 y > 6$ $2x + 3y > 6$ ?

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Answer 1 · 2015-04-06T01:11:46

First draw a lightly dashed version of the line $2 x + 3 y = 6$ $2x+3y=6$ , which is equivalent to $y = - \frac{2}{3} x + 2$ $y=-\frac{2}{3}x+2$ (a line with a slope of $- \frac{2}{3}$ $-2/3$ and a $y$ $y$ -intercept of $y = 2$ $y=2$ ...also note that the $x$ $x$ -intercept is $x = 3$ $x=3$ ).

Next, note that the point $(0, 0)$ $(0,0)$ does not satisfy the inequality $2 x + 3 y > 6$ $2x+3y>6$ . Therefore, shade in the "half-plane" on the other side of the line $2 x + 3 y = 6$ $2x+3y=6$ from the side that $(0, 0)$ $(0,0)$ is on. Make sure the line $2 x + 3 y = 6$ $2x+3y=6$ remains lightly dashed. It's not part of the solution set.

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How do you graph the inequality $2 x + 3 y > 6$ $2x + 3y > 6$ ?

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How do you graph the inequality $2 x + 3 y > 6$ $2x + 3y > 6$ ?