Human weight. A good approximation of the normal weight of a person 60 inches or

taller but not taller than 80 inches is given by w(x) = 5.5x - 220, where x is height in inches and w(x)

is weight in pounds.

(A) Describe how the graph of function w can be obtained from the graph of one of the basic

functions.

(B) Sketch a graph of function w using part (A) as an aid.

### (A) Graph of the Function \( w(x) = 5.5x - 220 \)

To describe how the graph of the function \( w(x) = 5.5x - 220 \) can be obtained from one of the basic functions, consider the following steps:

1. **Basic Function**: Start with the basic linear function, which is \( f(x) = x \). The graph of this function is a straight line with a slope of 1 passing through the origin.

2. **Slope Transformation**: The function \( w(x) = 5.5x - 220 \) has a slope of 5.5. This means that the graph is stretched vertically by a factor of 5.5 compared to \( f(x) = x \). So, the line will be steeper than the basic linear function.

3. **Vertical Shift**: The constant term \( -220 \) shifts the graph downward by 220 units. This is because when \( x = 0 \), the function value \( w(x) = -220 \).

Therefore, the graph of \( w(x) = 5.5x - 220 \) is a line with slope 5.5 that passes through the point \( (0, -220) \), and is steeper than the basic line \( f(x) = x \).

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### (B) Sketch of the Function \( w(x) = 5.5x - 220 \)

Here is a step-by-step description to sketch the graph of \( w(x) = 5.5x - 220 \):

1. **Start with the point where \( w(x) = 0 \)**:
   - Solve \( 5.5x - 220 = 0 \) for \( x \):
   \[
   5.5x = 220 \implies x = \frac{220}{5.5} = 40
   \]
   This tells us that the graph crosses the x-axis at \( (40, 0) \).

2. **Use another point**:
   - When \( x = 60 \) (a typical height in inches), we calculate:
   \[
   w(60) = 5.5 \times 60 - 220 = 330 - 220 = 110
   \]
   So, the point \( (60, 110) \) is also on the graph.

3. **Draw the Line**:
   - The graph is a straight line passing through \( (40, 0) \) and \( (60, 110) \), with a slope of 5.5. As the slope is positive, the line rises steeply as \( x \) increases.

I can also visualize and plot the graph if you'd like, based on this description.

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Would you like me to provide further details, or any specific points you want clarified?

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### Five Related Questions:
1. How does changing the slope in a linear function affect the graph?
2. What happens to the graph of \( w(x) = 5.5x - 220 \) if the constant is changed from -220 to -150?
3. Can you explain how to find the slope of a linear function from two points on the graph?
4. How can you interpret the real-world meaning of the slope and intercept in this context of height and weight?
5. How does the domain and range of this function relate to the problem?

### Tip:
Always check the slope and intercept of a linear equation to understand how the graph behaves—whether it rises, falls, and where it crosses the y-axis.

Human weight. A good approximation of the normal weight of a person 60 inches or taller but not taller than 80 inches is given by w(x) = 5.5x - 220, where x is height in inches and w(x) is weight in pounds.

(A) Describe how the graph of function w can be obtained from the graph of one of the basic functions.

(B) Sketch a graph of function w using part (A) as an aid.

Explore how to graph the linear function w(x) = 5.5x - 220, representing the relationship between height and weight for people 60 to 80 inches tall. Learn step-by-step how the slope and vertical shift affect the graph and get a visual representation of this real-world application. Suitable for Grades 9-12.

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