Question

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 \((x_1, y_1)\) is a point on the line and \(m\) is the slope. Given that the slope \(m\) is \(\frac{1}{9}\) and the point is \((-4, -7)\), we can substitute these values into the formula.

Here, \(x_1 = -4\) and \(y_1 = -7\).

Substituting the values into the point-slope form:

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

This simplifies to:

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

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

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