To find the equation of the line in point-slope form, we first need to determine the slope of the line that passes through the points \((-10, 7)\) and \((8, -7)\).
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's assign the points:
- \((x_1, y_1) = (-10, 7)\)
- \((x_2, y_2) = (8, -7)\)
Now plug in the values into the formula:
\[ m = \frac{-7 - 7}{8 - (-10)} = \frac{-14}{8 + 10} = \frac{-14}{18} \]
Now simplify \(\frac{-14}{18}\):
\[ m = \frac{-14 \div 2}{18 \div 2} = \frac{-7}{9} \]
Now that we have the slope \(m = -\frac{7}{9}\), we can write the equation of the line in point-slope form. The point-slope form of the equation of a line is given by:
\[ y - y_1 = m(x - x_1) \]
We will use the point \((-10, 7)\):
\[ y - 7 = -\frac{7}{9}(x - (-10)) \]
This simplifies to:
\[ y - 7 = -\frac{7}{9}(x + 10) \]
Thus, the equation of the line in point-slope form is:
\[ y - 7 = -\frac{7}{9}(x + 10) \]
This is the final answer.