Question
Find the slope \( m \) of the line through the following pair of points and draw the line through the points. \( (6,1),(5,2) \) Answer exactly. \( m= \)
Ask by Estrada Mejia. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The slope \( m \) of the line through the points \( (6, 1) \) and \( (5, 2) \) is \( -1 \).
Solution
It seems that I cannot directly draw the line through the points. However, I can describe how to do it.
To draw the line through the points \( (6, 1) \) and \( (5, 2) \):
1. **Plot the Points**:
- Mark the point \( (6, 1) \) on the Cartesian plane.
- Mark the point \( (5, 2) \) on the Cartesian plane.
2. **Draw the Line**:
- Use a ruler to connect the two points with a straight line.
3. **Slope Interpretation**:
- Since the slope \( m = -1 \), the line will descend from left to right, indicating that for every unit you move to the right, you move down one unit.
In summary, the slope of the line through the points \( (6, 1) \) and \( (5, 2) \) is \( m = -1 \).
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Simplify this solution Beyond the Answer
To find the slope \( m \) of the line through the points \( (6,1) \) and \( (5,2) \), we use the formula for slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Assigning \( (x_1, y_1) = (6, 1) \) and \( (x_2, y_2) = (5, 2) \), we get: \[ m = \frac{2 - 1}{5 - 6} = \frac{1}{-1} = -1 \] Thus, the slope \( m = -1 \). Now, to visualize the line, we can plot the two points on a coordinate plane. The point \( (6, 1) \) is to the right and slightly below the point \( (5, 2) \). Connecting these points shows a line that slopes downward from left to right, illustrating the negative slope of -1.
