3x - 2 < y

Question

x - y > 6
graph these

Answer 1

To graph the inequalities 3x - 2 < y and x - y > 6, we need to first graph their corresponding equations.

For the equation 3x - 2 = y, we can rearrange it to y = 3x - 2 and plot the points on a Cartesian plane as follows:

Let x = 0, then y = 3(0) - 2 = -2, giving us the point (0, -2).
Let x = 1, then y = 3(1) - 2 = 1, giving us the point (1, 1).

Plotting these points and drawing the line, we get:

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For the equation x - y = 6, we can rearrange it to y = x - 6 and plot the points on the same Cartesian plane:

Let x = 0, then y = 0 - 6 = -6, giving us the point (0, -6).
Let x = 1, then y = 1 - 6 = -5, giving us the point (1, -5).

Plotting these points and drawing the line, we get:

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Now, let's shade the regions that satisfy the inequalities.

For 3x - 2 < y, we need to shade the area below the line.

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For x - y > 6, we need to shade the area above the line.

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The area that satisfies both inequalities is the shaded region below the line y = 3x - 2 and above the line y = x - 6.

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