Question

or
A line has a slope of
1/9
and passes through the point (
–
4,
–
7). 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.

Answer 1

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

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

where \(m\) is the slope, and \((x_1, y_1)\) is the point the line passes through.

Given:
- Slope \(m = \frac{1}{9}\)
- Point \((-4, -7)\) implies \(x_1 = -4\) and \(y_1 = -7\)

Now we can substitute these values into the point-slope form:

\[
y - (-7) = \frac{1}{9}(x - (-4))
\]

This simplifies to:

\[
y + 7 = \frac{1}{9}(x + 4)
\]

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

\[
y + 7 = \frac{1}{9}(x + 4)
\]