- The given linear function is \(y = 16 + 0.5x\).
- Substitute each option's x-coordinate into the function:
- For \(x=5\), \(y=18.5\) (not 19.5).
- For \(x=8\), \(y=20\) (matches).
- For \(x=0\), \(y=16\) (not 18).
- For \(x=10\), \(y=21\) (not 21.5).
- The correct ordered pair is \((8, 20)\), which corresponds to option b.
- Final Answer: \(\boxed{b}\)
Explanation
- Problem Analysis
The problem provides a linear function \(y = 16 + 0.5x\) and asks which of the given ordered pairs \((x, y)\) fits this relationship. We are given the options a) \((5, 19.5)\), b) \((8, 20)\), c) \((0, 18)\), and d) \((10, 21.5)\). To identify the correct pair, we substitute the x-value of each option into the equation to see if the resulting y-value matches the y-coordinate provided in that option.
- Evaluating the Options
We check each option individually by substituting its x-coordinate into the expression \(16 + 0.5x\):
- For option a) \((5, 19.5)\):
Substituting \(x = 5\), we get \(y = 16 + 0.5(5) = 16 + 2.5 = 18.5\).
Since \(18.5
eq 19.5\), this pair does not satisfy the function.
- For option b) \((8, 20)\):
Substituting \(x = 8\), we get \(y = 16 + 0.5(8) = 16 + 4 = 20\).
Since \(20 = 20\), this pair satisfies the function.
- For option c) \((0, 18)\):
Substituting \(x = 0\), we get \(y = 16 + 0.5(0) = 16\).
Since \(16
eq 18\), this pair does not satisfy the function.
- For option d) \((10, 21.5)\):
Substituting \(x = 10\), we get \(y = 16 + 0.5(10) = 16 + 5 = 21\).
Since \(21
eq 21.5\), this pair does not satisfy the function.
- Conclusion
Based on our calculations, only the pair \((8, 20)\) yields the correct y-value when substituted into the linear function \(y = 16 + 0.5x\). Therefore, the correct option is b). The final answer is \(\boxed{b}\).
Examples
Linear functions are useful in real-life situations where a base value is modified by a constant rate. For instance, if a delivery company charges a flat fee of \(\$16\) plus \(\$0.50\) for every mile driven, the cost for a delivery of \(x\) miles is given by \(y = 16 + 0.5x\). By using this formula, you can calculate the total delivery cost for any distance. For example, if you need to travel 8 miles, the cost would be \(y = 16 + 0.5(8) = \$20\). Understanding this relationship helps in budgeting for services or estimating travel expenses effectively.