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

### Step 1: Find the 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:

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

Substitute the given points \((-5, 11)\) and \((5, -7)\) into the formula:

\[
m = \frac{-7 - 11}{5 - (-5)} = \frac{-18}{10} = -\frac{9}{5}
\]

### Step 2: Use the point-slope form of the line equation
The point-slope form of a line is:

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

Substitute the slope \(m = -\frac{9}{5}\) and one of the points, say \((-5, 11)\):

\[
y - 11 = -\frac{9}{5}(x - (-5))
\]

Simplify the equation:

\[
y - 11 = -\frac{9}{5}(x + 5)
\]

Distribute the slope:

\[
y - 11 = -\frac{9}{5}x - 9
\]

Add 11 to both sides to solve for \(y\):

\[
y = -\frac{9}{5}x - 9 + 11
\]

\[
y = -\frac{9}{5}x + 2
\]

### Final Answer:
The equation of the line is:

\[
y = -\frac{9}{5}x + 2
\]

Would you like further clarification or details?

### Related Questions:
1. How do you find the slope when given two points?
2. What is the point-slope form of a linear equation?
3. How do you convert the point-slope form to the slope-intercept form?
4. Can you find the equation of a line given just one point and the slope?
5. How would the equation change if the points were reversed?

### Tip:
The slope is the most crucial part when forming the equation of a line. Always ensure you calculate it accurately, as it affects the rest of the equation.

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) using the slope and point-slope form. This problem includes key algebraic concepts such as finding the slope and writing the equation in slope-intercept form. Suitable for students in Grades 8-10.

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