Question

There is a line that includes the point (6,
–
1) and 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.

Answer 1

To write the equation of a line in point-slope form, we 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 the point \((6, -1)\) and the slope \(m = -9\), we can plug these values into the formula:

1. Identify \(x_1\) and \(y_1\):
- \(x_1 = 6\)
- \(y_1 = -1\)

2. Substitute into the point-slope form formula:

\[
y - (-1) = -9(x - 6)
\]

This simplifies to:

\[
y + 1 = -9(x - 6)
\]

This is the equation of the line in point-slope form.

If you prefer it to be more explicit:

\[
y + 1 = -9(x - 6)
\]

is already in its simplified point-slope form. If you wish to rearrange it into slope-intercept form, you could distribute the \(-9\) and solve for \(y\), but the form requested was point-slope, which is:

\[
y + 1 = -9(x - 6)
\]

This is the final answer in point-slope form.