To represent the inequality \(5x - y > 1\) on a grid (or coordinate plane), we first need to rewrite it in a more useful form. We can rearrange the inequality to express \(y\) in terms of \(x\):
\[ 5x - y > 1 \implies -y > 1 - 5x \implies y < 5x - 1 \]
Now, we have the inequality \(y < 5x - 1\).
Steps to Plot the Inequality on a Grid:
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Graph the Boundary Line:
- The boundary line is given by the equation \(y = 5x - 1\). This is a straight line with a slope of 5 and a y-intercept of -1.
- To graph this line, find two points:
- If \(x = 0\): \[ y = 5(0) - 1 = -1 \quad \Rightarrow \quad (0, -1) \]
- If \(x = 1\): \[ y = 5(1) - 1 = 4 \quad \Rightarrow \quad (1, 4) \]
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Draw the Boundary Line:
- Since this is an inequality that uses "less than" (<), we draw a dashed line (indicating that the points on the line itself are not included).
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Shade the Appropriate Region:
- Since the inequality is \(y < 5x - 1\), we need to shade the region below the line. This region includes all the coordinates where \(y\) is less than the value calculated by \(5x - 1\).
Conclusion:
The ordered pair \((5, y)\) satisfies this inequality if the value of \(y\) is less than \(5(5) - 1 = 25 - 1 = 24\). Thus, any pair \((5, y)\) where \(y < 24\) would be in the shaded region below the dashed line.
To summarize:
- Boundary line: Dashed line for \(y = 5x - 1\)
- Shaded area: Below the boundary line
- Ordered pairs: Valid points in the shaded area, such as \( (5, 23), (5, 10), (5, -5) \), etc.
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