Find the slope of the line passing through the points (3, 8) and (7, - 7).

1 answer

To find the slope \( m \) of the line passing through the points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula:

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

For the points \((3, 8)\) and \((7, -7)\), we have:

  • \(x_1 = 3\), \(y_1 = 8\)
  • \(x_2 = 7\), \(y_2 = -7\)

Substituting these values into the slope formula gives:

\[ m = \frac{-7 - 8}{7 - 3} \]

Calculating the numerator:

\[ -7 - 8 = -15 \]

Calculating the denominator:

\[ 7 - 3 = 4 \]

Now, substituting these results into the slope formula:

\[ m = \frac{-15}{4} \]

Thus, the slope of the line passing through the points \((3, 8)\) and \((7, -7)\) is

\[ \boxed{-\frac{15}{4}}. \]