Question

identifying the graph of an inequality
which is the graph of $2x - 4y > 6$?
four graphs with coordinate planes and lines, each with a shaded region and a radio button below

Explanation:

Step1: Rearrange to slope-intercept form

Start with the given inequality:
$$2x - 4y > 6$$
Subtract $2x$ from both sides:
$$-4y > -2x + 6$$
Divide by $-4$ (reverse inequality sign):
$$y < \frac{1}{2}x - \frac{3}{2}$$

Step2: Identify line properties

The boundary line is $y = \frac{1}{2}x - \frac{3}{2}$, which has a y-intercept of $-\frac{3}{2}$ and slope $\frac{1}{2}$. Since the inequality is $<$, the line is dashed, and we shade below the line.

Step3: Match to graph

Find the graph with a dashed line following $y = \frac{1}{2}x - \frac{3}{2}$ and shading below the line.

Answer:

The correct graph is the second one from the left (dashed line, shading below the line, passing through intercepts $(3,0)$ and $(0, -1.5)$)