Question

There is a line that includes the point (4,1) and has a slope of
–
1
9
. What is its equation in point-slope form?

Answer 1

To write the equation of a line in point-slope form, we 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 \((4, 1)\) and a slope of \(-\frac{1}{9}\), we can substitute these values into the formula:

- \(x_1 = 4\)
- \(y_1 = 1\)
- \(m = -\frac{1}{9}\)

Substituting these values into the point-slope form gives us:

\[
y - 1 = -\frac{1}{9}(x - 4)
\]

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