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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