Question

A line has a slope of 1/5 and passes through the point (6,–4). What is its equation in point-slope form?

Answer 1

The point-slope form of the equation of a line is given by the formula:

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

where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.

In your case, the slope \( m \) is \( \frac{1}{5} \) and the point is \( (6, -4) \).

Substituting these values into the point-slope formula:

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

This simplifies to:

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

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

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