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The image shows a line segment plotted on a coordinate grid between two points: \((-2, 1)\) and \((4, 3)\). I can help with various aspects related to this line, such as finding its slope, equation, midpoint, or distance between the two points.

### Let's start with some calculations:

1. **Slope of the Line**: The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Plugging in the values \((-2, 1)\) and \((4, 3)\):
   \[
   m = \frac{3 - 1}{4 - (-2)} = \frac{2}{6} = \frac{1}{3}
   \]
   So, the slope of the line is \( \frac{1}{3} \).

2. **Equation of the Line**: Using the point-slope form of the line equation:
   \[
   y - y_1 = m(x - x_1)
   \]
   With slope \( m = \frac{1}{3} \) and point \((-2, 1)\), we have:
   \[
   y - 1 = \frac{1}{3}(x - (-2)) = \frac{1}{3}(x + 2)
   \]
   Expanding this:
   \[
   y - 1 = \frac{1}{3}x + \frac{2}{3}
   \]
   \[
   y = \frac{1}{3}x + \frac{5}{3}
   \]
   So, the equation of the line is \( y = \frac{1}{3}x + \frac{5}{3} \).

3. **Midpoint**: The midpoint \( M \) of a line segment between two points is given by:
   \[
   M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
   \]
   For the points \((-2, 1)\) and \((4, 3)\):
   \[
   M = \left( \frac{-2 + 4}{2}, \frac{1 + 3}{2} \right) = (1, 2)
   \]
   So, the midpoint is \( (1, 2) \).

4. **Distance between the Points**: The distance \( d \) between two points is given by the distance formula:
   \[
   d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]
   Plugging in the values \((-2, 1)\) and \((4, 3)\):
   \[
   d = \sqrt{(4 - (-2))^2 + (3 - 1)^2} = \sqrt{(6)^2 + (2)^2} = \sqrt{36 + 4} = \sqrt{40} = 2\sqrt{10} \approx 6.32
   \]
   The distance between the two points is approximately 6.32 units.

### Do you want more details on any of these calculations?

Here are 5 questions to expand on this:

1. Would you like to explore how to convert the equation into different forms (slope-intercept or standard)?
2. Should we calculate the angle of the line with respect to the x-axis?
3. Would you like to know how this line would be graphed on a different scale or coordinate plane?
4. Are you interested in calculating the area of the triangle formed by these two points and the origin?
5. Should we discuss how the line behaves in different quadrants or transformations of the graph?

#### Tip: When finding the slope between two points, always check if the difference in x-values is zero. If it is, the line is vertical, and its slope is undefined.

Given two points (-2, 1) and (4, 3) on a coordinate plane, find the slope, equation of the line, midpoint, and distance between the points.

This problem involves finding the slope, equation of the line, midpoint, and distance between the points (-2, 1) and (4, 3) on a coordinate plane. The solution includes key geometry concepts like the slope formula, equation of a line, midpoint formula, and distance formula. Suitable for students in Grades 8-10.

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