Question

A line includes the points (1,6) and (10,3). 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 calculate the slope (m) of the line that passes through the points (1, 6) and (10, 3).

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Plugging in the coordinates of the points (1, 6) and (10, 3):

\[
m = \frac{3 - 6}{10 - 1} = \frac{-3}{9} = -\frac{1}{3}
\]

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

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

Using the slope \( m = -\frac{1}{3} \) and one of the points, let's use (1, 6):

\[
y - 6 = -\frac{1}{3}(x - 1)
\]

Thus, the equation of the line in point-slope form is:

\[
y - 6 = -\frac{1}{3}(x - 1)
\]