Question

The points (–10,7) and (8,–7) fall on a particular line. What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

Answer 1

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.