To graph the inequality 1 - 1/4x ≥ -1, plot the y-intercept at 1, use the slope of -1/4 to find another point, draw a solid line for 'equal to', and shade above the line, indicating 'greater than'.
To graph the inequality 1 - \( \frac{1}{4}x \) greater or equal to -1, we follow these steps:
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- Rewrite the inequality in slope-intercept form: \( y \geq 1 - \frac{1}{4}x \).
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- Identify the y-intercept (1) and the slope (-1/4).
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- Plot the y-intercept on the y-axis.
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- From the y-intercept, use the slope to find another point. Since the slope is -1/4, move down 1 unit and right 4 units from the y-intercept.
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- Draw a solid line through these points because the inequality includes 'equal to'.
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- Shade the area above the line, since y is greater than the expression.
The graph represents all the solutions to the inequality. Any point in the shaded area satisfies the inequality. Use a test point (like 0,0) to confirm the correct shading direction.