Question

AB has endpoints A(8, k) and B(7, -3). The slope of AB is 5. What is K?

Answer 1

To find the value of \( k \) given the endpoints \( A(8, k) \) and \( B(7, -3) \) with a slope of 5, we start with the formula for the slope of a line between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

For our points \( A(8, k) \) and \( B(7, -3) \), we can substitute:
- \( x_1 = 8 \), \( y_1 = k \)
- \( x_2 = 7 \), \( y_2 = -3 \)

Now, plug these values into the slope formula:

\[
5 = \frac{-3 - k}{7 - 8}
\]

Simplifying the denominator:

\[
5 = \frac{-3 - k}{-1}
\]

This can be simplified to:

\[
5 = 3 + k
\]

Now, solving for \( k \):

\[
k = 5 - 3
\]
\[
k = 2
\]

Thus, the value of \( k \) is \( \boxed{2} \).