Question

A line includes the points (6,1) and (1,5). What is its equation in point-slope form?

Answer 1

To write the equation of a line in point-slope form, we first need to determine the slope of the line. The slope \( m \) can be calculated using the formula:

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

Letting \((x_1, y_1) = (6, 1)\) and \((x_2, y_2) = (1, 5)\):

\[
m = \frac{5 - 1}{1 - 6} = \frac{4}{-5} = -\frac{4}{5}
\]

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

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

Using the point \((6, 1)\) and the slope \( -\frac{4}{5} \):

\[
y - 1 = -\frac{4}{5}(x - 6)
\]

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

\[
y - 1 = -\frac{4}{5}(x - 6)
\]