Question

There is a line that includes the point (–8,3) and has a slope of –1/2
. What is its equation in point-slope form?

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.

In this case, you have the point \( (x_1, y_1) = (-8, 3) \) and the slope \( m = -\frac{1}{2} \).

Substituting these values into the point-slope formula gives:

\[
y - 3 = -\frac{1}{2}(x - (-8))
\]
\[
y - 3 = -\frac{1}{2}(x + 8)
\]

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

\[
y - 3 = -\frac{1}{2}(x + 8)
\]