Question

A line has a slope of
–
3 and includes the points (k,
–
9) and (6,0). What is the value of k?

Answer 1

To find the value of \( k \), we will use the slope formula. The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

In this case, we have two points: \((k, -9)\) and \((6, 0)\), and the slope \( m = -3 \).

Let’s assign our points:
- \( (x_1, y_1) = (k, -9) \)
- \( (x_2, y_2) = (6, 0) \)

Using the slope formula, we can set up the equation:

\[
-3 = \frac{0 - (-9)}{6 - k}
\]

Simplifying the numerator:

\[
-3 = \frac{0 + 9}{6 - k}
\]
\[
-3 = \frac{9}{6 - k}
\]

Next, we can cross-multiply to eliminate the fraction:

\[
-3(6 - k) = 9
\]

Distributing the -3:

\[
-18 + 3k = 9
\]

Next, we add 18 to both sides:

\[
3k = 9 + 18
\]
\[
3k = 27
\]

Now, divide by 3:

\[
k = \frac{27}{3} = 9
\]

Thus, the value of \( k \) is

\[
\boxed{9}
\]