Describe how the graph of 

​h(x)equals=minus−33xplus+66 

can be obtained from one of the basic graphs. Then graph the function.

The function \( h(x) = -3x + 66 \) is a linear function, which can be related to the basic graph of a linear function \( f(x) = x \), which is a straight line passing through the origin (0, 0) with a slope of 1.

### Steps to Obtain the Graph of \( h(x) = -3x + 66 \):
1. **Start with the basic graph** of the identity function \( f(x) = x \), which has a slope of 1 and passes through the origin (0, 0).
   
2. **Apply a reflection over the x-axis**: Since the slope of \( h(x) \) is -3, this is a steeper line, and the negative sign indicates a reflection across the x-axis. This changes the slope from 1 to -3, which tilts the graph downward.

3. **Apply a vertical translation**: The "+66" shifts the entire line upward by 66 units. So, instead of passing through the origin, the new line passes through the point (0, 66).

The resulting graph is a straight line with a slope of -3, indicating that for every 1 unit increase in \( x \), \( y \) decreases by 3. The y-intercept is at (0, 66).

I will now plot the graph of \( h(x) = -3x + 66 \).It seems like I can’t do more advanced data analysis right now. Please try again later. 

You can still sketch the graph manually by following these steps:
- Start with the basic line for \( f(x) = x \).
- Reflect the line downward (as the slope is -3).
- Shift the entire line upward by 66 units.

Would you like more details on plotting manually, or any other clarification? 

Here are 5 related questions:
1. How do you find the slope of a linear function from its equation?
2. What are the effects of changing the slope on the graph of a line?
3. How do vertical and horizontal translations affect linear functions?
4. What is the geometric meaning of the y-intercept?
5. How can we interpret real-world problems using linear functions?

**Tip**: When graphing a linear equation, focus first on the slope and intercept to sketch the line easily.

Describe how the graph of h(x) = -3x + 66 can be obtained from one of the basic graphs. Then graph the function.

Learn how to graph the linear function h(x) = -3x + 66 by applying graph transformations to the basic linear function. This problem focuses on identifying the slope, applying reflection across the x-axis, and vertical translation. Suitable for students in Grades 8-10.

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