Question

A line that includes the point (2,
–
1) has a slope of
–
1
5
. What is its equation in point-slope form?
Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
y–
=
x–

Answer 1

To write the equation of a line in point-slope form (\(y - y_1 = m(x - x_1)\)), you need a slope (\(m\)) and a point (\(x_1, y_1\)) through which the line passes.

In your case:
- The point is \((x_1, y_1) = (2, -1)\)
- The slope is \(m = -\frac{1}{5}\)

Substituting these values into the point-slope formula gives:

\[
y - (-1) = -\frac{1}{5}(x - 2)
\]

This simplifies to:

\[
y + 1 = -\frac{1}{5}(x - 2)
\]

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

\[
y + 1 = -\frac{1}{5}(x - 2)
\]

This equation uses integers and proper fractions as specified.