Question

The points (5,5) and (3,9) 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 \( m \) of the line that passes through the points (5, 5) and (3, 9).

The formula for the slope \( m \) between 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 coordinates of our points:

\((x_1, y_1) = (5, 5)\) and \((x_2, y_2) = (3, 9)\),

we have:

\[
m = \frac{9 - 5}{3 - 5} = \frac{4}{-2} = -2
\]

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

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

We can choose either point for \((x_1, y_1)\). Let's use the point (5, 5):

\[
y - 5 = -2(x - 5)
\]

This is the equation of the line in point-slope form:

\[
y - 5 = -2(x - 5)
\]

This equation is already simplified and in the correct format. Thus, the final answer is:

\[
\boxed{y - 5 = -2(x - 5)}
\]