Question

A line has a slope of
–
6 and includes the points (
–
8,p) and (
–
9,
–
3). What is the value of p?
p=

Answer 1

To find the value of \( p \), we can use the formula for the slope of a line, which is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Given the slope \( m = -6 \) and the points \((-8, p)\) and \((-9, -3)\), we can set \( (x_1, y_1) = (-9, -3) \) and \( (x_2, y_2) = (-8, p) \).

Substituting the values into the slope formula:

\[
-6 = \frac{p - (-3)}{-8 - (-9)}
\]

This simplifies to:

\[
-6 = \frac{p + 3}{-8 + 9}
\]
\[
-6 = \frac{p + 3}{1}
\]

Thus, we can rewrite the equation as:

\[
-6 = p + 3
\]

To solve for \( p \), subtract 3 from both sides:

\[
p = -6 - 3
\]
\[
p = -9
\]

So, the value of \( p \) is:

\[
\boxed{-9}
\]