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 the 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 (\(x_1, y_1\)) = \( (4, -7) \)

Now, substituting these values into the point-slope form equation:

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

This simplifies to:

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

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

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