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10 Fill in the Blank 1 point Convert the function \( y=4.5+0.75(x-12) \) into slope-intercept form and identify the rate of change. The rate of change is type your answer...

Ask by Cole Mathis. in the United States
Feb 03,2025

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Answer

The rate of change is 0.75.

Solution

The rate of change in the function \( y = 4.5 + 0.75(x - 12) \) is **0.75**. **Explanation:** To convert the given function into slope-intercept form (\( y = mx + b \)): \[ \begin{align*} y &= 4.5 + 0.75(x - 12) \\ &= 4.5 + 0.75x - 0.75 \times 12 \\ &= 4.5 + 0.75x - 9 \\ &= 0.75x - 4.5 \end{align*} \] Here, the slope-intercept form is \( y = 0.75x - 4.5 \), where: - **Slope (\( m \))**: **0.75** (This is the rate of change) - **Y-intercept (\( b \))**: -4.5 So, the **rate of change is 0.75**.

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Bonus Knowledge

To convert the function \( y = 4.5 + 0.75(x - 12) \) into slope-intercept form (which is \( y = mx + b \)), let's distribute the 0.75: 1. Distributing gives us \( y = 4.5 + 0.75x - 9 \). 2. Combining like terms results in \( y = 0.75x - 4.5 \). In this equation, the slope (rate of change) is 0.75. So, the rate of change is 0.75. And there you have it—your slope-intercept form is all set! Keep an eye out for those transformations; they can sneak up on you when you're dealing with different formats!

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