Question

A line has a slope of
–
5 and passes through the point (
–
4,
–
1). 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 \( m \) is the slope of the line, and \((x_1, y_1)\) is a point on the line.

Given:
- Slope (\( m \)) = -5
- Point (\( x_1, y_1 \)) = (-4, -1)

Substituting these values into the formula:

\[
y - (-1) = -5(x - (-4))
\]

This simplifies to:

\[
y + 1 = -5(x + 4)
\]

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

\[
y + 1 = -5(x + 4)
\]