which is the graph of 2x - 4y > 6?

Explanation:

Step1: Rewrite the inequality in slope - intercept form

First, solve (2x - 4y>6) for (y). Subtract (2x) from both sides: (-4y>-2x + 6). Then divide by (-4). When dividing an inequality by a negative number, the direction of the inequality sign changes. So (y<\frac{1}{2}x-\frac{3}{2}).

Step2: Analyze the boundary line

The boundary line of the inequality (y<\frac{1}{2}x - \frac{3}{2}) is (y = \frac{1}{2}x-\frac{3}{2}), which has a slope of (\frac{1}{2}) and a (y) - intercept of (-\frac{3}{2}). Since the inequality is (y<\frac{1}{2}x-\frac{3}{2}), the boundary line is dashed (because the points on the line are not included in the solution set).

Step3: Test a point

We can test the point ((0,0)). Substitute (x = 0) and (y = 0) into the original inequality (2x-4y>6). We get (2(0)-4(0)=0), and (0\not>6). So the region that does not contain the point ((0,0)) is the solution region.

Answer:

The graph with a dashed line having a slope of (\frac{1}{2}), (y) - intercept of (-\frac{3}{2}), and the region below the line (not containing the origin ((0,0))) is the correct graph.