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The graphs given above show data representing the percentage of women and the percentage of men on weight-loss diets for three selected years after 1987. The lines were drawn to pass through or be near the three points. Estimate the slope and the equation for the line for the percentage of men on diets. M= and the equation of the line in slope intercept form:

Let's break down the graph step by step to estimate the slope and determine the equation for the line representing the percentage of men on weight-loss diets.

### Analyzing the Graph:
- The graph for men is the lower line in orange.
- The key points on the graph for men are labeled as:
  - \( (10, 10) \)
  - \( (16, 8.8) \)

### Step 1: Find the slope (M)
The slope formula is given by:

\[
M = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (10, 10) \) and \( (16, 8.8) \):

\[
M = \frac{8.8 - 10}{16 - 10} = \frac{-1.2}{6} = -0.2
\]

So, the slope \( M \) is \(-0.2\).

### Step 2: Find the equation of the line in slope-intercept form

The slope-intercept form of a line is:

\[
y = Mx + b
\]

Now, substitute \( M = -0.2 \) and use one of the given points, say \( (10, 10) \), to solve for the intercept \( b \).

\[
10 = -0.2(10) + b
\]

\[
10 = -2 + b
\]

\[
b = 12
\]

### Final Equation:
The equation of the line for the percentage of men on diets is:

\[
y = -0.2x + 12
\]

Would you like further details or clarification on any step?

Here are some additional questions to deepen your understanding:
1. What is the significance of the slope in this context?
2. How would the equation change if a different point was used to calculate the intercept?
3. How would the line for women compare if you calculated its slope and intercept?
4. What does the negative slope indicate about the trend in the percentage of men on diets?
5. Can you predict the percentage of men on diets in future years using the equation?

**Tip:** When calculating the equation of a line, always verify your intercept by plugging another known point into the equation to ensure consistency.

Learn how to estimate the slope and equation of the line representing the percentage of men on weight-loss diets based on data for three selected years after 1987. We use the slope formula and the slope-intercept form equation to find the equation for men’s diets. Suitable for students in Grades 9-12.

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