Question

what is the slopes
1,9 and -1,6
4,-1 and -2,2
-4,-6 and 8,9

Answer 1

To find the slope of a line given two points, you can use the formula:

\[
\text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1}
\]

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

Let's calculate the slopes for each pair of points you provided.

1. **Points (1, 9) and (-1, 6)**:
- \(x_1 = 1\), \(y_1 = 9\)
- \(x_2 = -1\), \(y_2 = 6\)
- Slope \(m = \frac{6 - 9}{-1 - 1} = \frac{-3}{-2} = \frac{3}{2}\)

2. **Points (4, -1) and (-2, 2)**:
- \(x_1 = 4\), \(y_1 = -1\)
- \(x_2 = -2\), \(y_2 = 2\)
- Slope \(m = \frac{2 - (-1)}{-2 - 4} = \frac{3}{-6} = -\frac{1}{2}\)

3. **Points (-4, -6) and (8, 9)**:
- \(x_1 = -4\), \(y_1 = -6\)
- \(x_2 = 8\), \(y_2 = 9\)
- Slope \(m = \frac{9 - (-6)}{8 - (-4)} = \frac{15}{12} = \frac{5}{4}\)

Summarizing the slopes:
1. For points (1, 9) and (-1, 6), the slope is \(\frac{3}{2}\).
2. For points (4, -1) and (-2, 2), the slope is \(-\frac{1}{2}\).
3. For points (-4, -6) and (8, 9), the slope is \(\frac{5}{4}\).