Questions: Graph the following inequality. 3x + 4y > 12

Transcript text: Graph the following inequality. \[ 3 x+4 y>12 \]

Solution

Solution Steps

Step 1: Rewrite the inequality in slope-intercept form

The given inequality is: \[ 3x + 4y > 12 \]

First, we rewrite it in slope-intercept form $ y = mx + b $: \[ 4y > -3x + 12 \] \[ y > -\frac{3}{4}x + 3 \]

Step 2: Identify the boundary line

The boundary line for the inequality is: \[ y = -\frac{3}{4}x + 3 \]

Step 3: Determine the region to shade

Since the inequality is $ y > -\frac{3}{4}x + 3 $, we will shade the region above the line.

Final Answer

The inequality $ 3x + 4y > 12 $ can be represented by the line $ y = -\frac{3}{4}x + 3 $ with the region above the line shaded.

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = (-3/4)x + 3"], "latex_expressions": ["$y = -\\frac{3}{4}x + 3$"]}

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