Question

A line with a slope of
–
1
3
passes through the point (6,5). 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, we use the formula:

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

where \((x_1, y_1)\) is the point the line passes through and \(m\) is the slope.

Given:
- Slope \(m = -\frac{1}{3}\)
- Point \((x_1, y_1) = (6, 5)\)

Using these values, we plug them into the point-slope formula:

\[
y - 5 = -\frac{1}{3}(x - 6)
\]

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

\[
y - 5 = -\frac{1}{3}(x - 6)
\]

If you need me to rearrange it or convert it to another form, just let me know!