Question

A line with a slope of
–
5 passes through the point (
–
7,6). What is its equation in point-slope form?

Answer 1

To write the equation of a line in point-slope form, we 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 \( (x_1, y_1) = (-7, 6) \)

Plugging these values into the point-slope formula, we get:

\[
y - 6 = -5(x - (-7))
\]

This simplifies to:

\[
y - 6 = -5(x + 7)
\]

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

\[
y - 6 = -5(x + 7)
\]