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–

1 answer

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.