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

To write the equation of a line in point-slope form, you can use the formula:

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

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

In your case, the slope \( m \) is \( \frac{1}{5} \) and the point \( (x_1, y_1) \) is \( (6, -4) \).

Plugging 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:

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