Questions: Graph the inequality. 5x + y < 2

Transcript text: Graph the inequality. \[ 5 x+y<2 \]

Solution

Solution Steps

Step 1: Convert the Inequality to an Equation

To graph the inequality $5x + y < 2$ , we first convert it to the equation $5x + y = 2$ .

Step 2: Solve for

y

Rearrange the equation to solve for $y$ : $y = -5x + 2$

Step 3: Determine the Boundary Line

The boundary line for the inequality is $y = -5x + 2$ . This line will be dashed in the graph because the inequality is strict ( $<$ ).

Step 4: Determine the Shaded Region

Since the inequality is $5x + y < 2$ , the region below the line $y = -5x + 2$ will be shaded.

Final Answer

The inequality $5x + y < 2$ is represented by the region below the dashed line $y = -5x + 2$ .

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -10, "ymax": 10}, "commands": ["y = -5x + 2"], "latex_expressions": [" $y = -5x + 2$ "]}

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