To graph the inequality \( 2x - 7y < -14 \), you can follow these steps:
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Convert the inequality to an equation: Start by turning the inequality into an equation to find the boundary line. Set \( 2x - 7y = -14 \).
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Find intercepts: This is helpful for graphing the line.
- x-intercept: Set \( y = 0 \) and solve for \( x \): \[ 2x - 7(0) = -14 \implies 2x = -14 \implies x = -7. \] So, the x-intercept is \((-7, 0)\).
- y-intercept: Set \( x = 0 \) and solve for \( y \): \[ 2(0) - 7y = -14 \implies -7y = -14 \implies y = 2. \] So, the y-intercept is \((0, 2)\).
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Plot the line: Draw the line that passes through the points \((-7, 0)\) and \((0, 2)\). Since the inequality is \( < \), you will use a dashed line to indicate that points on the line are not included in the solution.
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Test a point: To determine which side of the line to shade, choose a test point that is not on the line. The point \((0, 0)\) is a good choice: \[ 2(0) - 7(0) < -14 \implies 0 < -14. \] This inequality is false, so we do not shade the region that includes \((0, 0)\). Instead, we shade the opposite side of the line.
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Final shading: Shade the region of the graph that is below the dashed line, as this represents all the points that satisfy the inequality \( 2x - 7y < -14 \).
Coordinates:
- X-intercept: \((-7, 0)\)
- Y-intercept: \((0, 2)\)
- Test point: \((0, 0)\)
These steps will help you accurately graph the inequality \( 2x - 7y < -14 \) on a coordinate plane.