Question

W.2 Find the slope from two points
VZG
Find the slope of the line that passes through (9, 4) and (2, 10).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer 1

To find the slope \( m \) of the line that passes through the two points \( (x_1, y_1) \) and \( (x_2, y_2) \), you can use the slope formula:

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

For the points \( (9, 4) \) and \( (2, 10) \):
- \( x_1 = 9 \)
- \( y_1 = 4 \)
- \( x_2 = 2 \)
- \( y_2 = 10 \)

Plugging in these values into the slope formula:

\[
m = \frac{10 - 4}{2 - 9}
\]

Calculating the differences:

\[
m = \frac{6}{-7}
\]

Thus, the slope simplifies to:

\[
m = -\frac{6}{7}
\]

So the slope of the line that passes through the points \( (9, 4) \) and \( (2, 10) \) is

\[
\boxed{-\frac{6}{7}}
\]