Question

A line that includes the point (4,10) has a slope of
–
9. 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 a line in point-slope form, you can 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:
- Point \( (4, 10) \) \(\Rightarrow (x_1, y_1) = (4, 10)\)
- Slope \( m = -9 \)

Now substituting these values into the point-slope form:

\[
y - 10 = -9(x - 4)
\]

This is the equation of the line in point-slope form. You can leave it as is or you can simplify further if needed, but in this case, it's already in the requested form.

So the final answer is:

\[
y - 10 = -9(x - 4)
\]