https://file.aiquickdraw.com/mathbot/file/172743943812509g6tm5g.jpg

The image shows a straight line on a graph, and the question asks to find the values of \( m \) (the slope) and \( b \) (the y-intercept) of the line. Here's how we can solve this:

1. **Find the slope \( m \):**
   The slope of a line is calculated using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   We need two points on the line. From the graph, we can identify:
   - Point 1: \( (0, 10) \) (the y-intercept)
   - Point 2: \( (2, 6) \)

   Using these points:
   \[
   m = \frac{6 - 10}{2 - 0} = \frac{-4}{2} = -2
   \]

2. **Find the y-intercept \( b \):**
   The y-intercept is where the line crosses the y-axis. From the graph, it's clear the line crosses at \( (0, 10) \), so \( b = 10 \).

Thus, the values of \( m \) and \( b \) are:
\[
m = -2, \quad b = 10
\]

Would you like more details or have any questions about these calculations?

Here are 5 related questions you can explore:
1. How do you find the slope of a line if given different points?
2. What happens to a line if the slope is positive vs. negative?
3. Can you explain the relationship between the slope and the steepness of a line?
4. How do parallel and perpendicular slopes relate to each other?
5. How can the equation of a line change if shifted up or down on the y-axis?

**Tip**: When identifying the slope, always choose two points that are easy to read from the graph to avoid mistakes in calculations.

Find the values of m and b for the line shown on the graph.

Learn how to find the slope (m) and y-intercept (b) of a line using a graph. This problem uses the slope formula and the y-intercept concept, making it suitable for students in Grades 8-10.

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