Question

A line that includes the point (9,
–
2) has a slope of
–
1
8
. 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.
y–
=
x–

Answer 1

To write the equation of the line in point-slope form using the point (9, -2) and a slope of -\(\frac{1}{8}\), you can use the point-slope formula:

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

Where:
- \((x_1, y_1)\) is the point on the line,
- \(m\) is the slope.

Here, \((x_1, y_1) = (9, -2)\) and \(m = -\frac{1}{8}\). Plugging these values into the formula gives:

\[
y - (-2) = -\frac{1}{8}(x - 9)
\]

This can be simplified to:

\[
y + 2 = -\frac{1}{8}(x - 9)
\]

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

\[
y + 2 = -\frac{1}{8}(x - 9)
\]

If you want to write it in the format you provided:

\[
y - (-2) = -\frac{1}{8}(x - 9)
\]

In relation to the structure you provided, we can write it as:

\[
y - (-2) = -\frac{1}{8}(x - 9)
\]

This essentially means:

\[
y + 2 = -\frac{1}{8}(x - 9)
\]

So, if you were looking for a specific way of writing it, the point-slope equation is correctly expressed.