You have provided two points: \((1, -7)\) and \((7, 0)\). Based on these points, I assume you may want to find one or more of the following:

1. **The slope of the line** that passes through these points.
2. **The equation of the line** that passes through these points.
3. **The distance between the two points**.
4. **The midpoint** between the two points.

Let’s go through each one.

### 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:

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

Substituting the values:

\[
m = \frac{0 - (-7)}{7 - 1} = \frac{7}{6}
\]

### 2. Equation of the Line
Using the point-slope form of a line equation:

\[
y - y_1 = m(x - x_1)
\]

Substitute \((x_1, y_1) = (1, -7)\) and \(m = \frac{7}{6}\):

\[
y + 7 = \frac{7}{6}(x - 1)
\]

Simplifying this:

\[
y + 7 = \frac{7}{6}x - \frac{7}{6}
\]
\[
y = \frac{7}{6}x - \frac{7}{6} - 7
\]
\[
y = \frac{7}{6}x - \frac{49}{6}
\]

So, the equation of the line is:

\[
y = \frac{7}{6}x - \frac{49}{6}
\]

### 3. Distance Between the Points
The distance \(d\) between two points is given by the formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the values:

\[
d = \sqrt{(7 - 1)^2 + (0 - (-7))^2} = \sqrt{6^2 + 7^2} = \sqrt{36 + 49} = \sqrt{85}
\]

So, the distance between the two points is \(\sqrt{85} \approx 9.22\).

### 4. Midpoint Between the Points
The midpoint \(M\) between two points is calculated as:

\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Substituting the values:

\[
M = \left( \frac{1 + 7}{2}, \frac{-7 + 0}{2} \right) = \left( \frac{8}{2}, \frac{-7}{2} \right) = (4, -\frac{7}{2})
\]

So, the midpoint is \((4, -\frac{7}{2})\).

---

Would you like more details on any of these steps or have any specific questions?

Here are 5 related questions to consider:
1. How do you calculate the slope of a perpendicular line through these points?
2. Can you convert the equation of the line into standard form?
3. How would the line equation change if the points were reversed?
4. How can we find the equation of a parallel line passing through another point?
5. What is the area of a triangle formed by these points and the origin?

**Tip:** When working with slopes, remember that perpendicular lines have slopes that are negative reciprocals of each other.

Explore how to calculate the slope, equation of the line, distance, and midpoint for the points (1, -7) and (7, 0) using analytical geometry formulas. This detailed solution involves the slope formula, point-slope form, distance formula, and midpoint formula, making it ideal for students in Grades 9-11.

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