Question

The points (5,5) and (3,9) fall on a particular line. What is its equation in point-slope form?

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 given points (5, 5) and (3, 9).

The slope \( m \) can be calculated using the formula:

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

Here, we can let \( (x_1, y_1) = (5, 5) \) and \( (x_2, y_2) = (3, 9) \). Plugging in the values:

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

Now that we have the slope \( m = -2 \), we can use one of the points, say (5, 5), to write the equation in point-slope form, which is given by:

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

Using the point (5, 5) and our calculated slope \( -2 \):

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

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

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