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To find the equation of a line passing through two points \((-5, 11)\) and \((5, -7)\), we can follow these steps:

### Step 1: Calculate the slope \(m\)
The slope of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the values of the points \((-5, 11)\) and \((5, -7)\):
\[
m = \frac{-7 - 11}{5 - (-5)} = \frac{-18}{5 + 5} = \frac{-18}{10} = -\frac{9}{5}
\]

### Step 2: Use the point-slope form
The equation of a line in point-slope form is:
\[
y - y_1 = m(x - x_1)
\]
We can use either of the points. Let's use \((-5, 11)\). Substituting the slope and the point:
\[
y - 11 = -\frac{9}{5}(x - (-5))
\]
Simplify:
\[
y - 11 = -\frac{9}{5}(x + 5)
\]
Distribute the slope:
\[
y - 11 = -\frac{9}{5}x - 9
\]
Add 11 to both sides:
\[
y = -\frac{9}{5}x - 9 + 11
\]
\[
y = -\frac{9}{5}x + 2
\]

### Final Equation:
The equation of the line is:
\[
y = -\frac{9}{5}x + 2
\]

Let me know if you want more details or have any questions!

Here are five related questions:
1. How do you convert a line equation from point-slope form to slope-intercept form?
2. What is the general form of a linear equation?
3. How can you find the slope if the points involve fractions?
4. How would the equation change if one of the points were on the y-axis?
5. What is the significance of the slope being negative?

**Tip:** If the slope is negative, it means the line is decreasing (sloping downwards) as you move from left to right.

Find the equation of the line through the points (-5, 11) and (5, -7).

Learn how to find the equation of a line passing through the points (-5, 11) and (5, -7). This problem covers key algebraic concepts such as slope calculation and converting between point-slope and slope-intercept forms. Suitable for Grades 8-10.

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