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Find the slope of the line that passes through (3, 8) and (10, 4).

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

3 answers

To find the slope of the line that passes through the points \((3, 8)\) and \((10, 4)\), we can use the formula for the slope \(m\):

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

Here, the points are given as:

  • \((x_1, y_1) = (3, 8)\)
  • \((x_2, y_2) = (10, 4)\)

Substituting the values into the slope formula:

\[ m = \frac{4 - 8}{10 - 3} \]

Now, calculating the numerator and the denominator:

\[ m = \frac{-4}{7} \]

Thus, the slope of the line that passes through the points \((3, 8)\) and \((10, 4)\) is:

\[ \boxed{-\frac{4}{7}} \]

Find the slope of the line that passes through (3, 11) and (6, 9).

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

To find the slope of the line that passes through the points \((3, 11)\) and \((6, 9)\), we can use the slope formula:

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

For the given points:

  • \((x_1, y_1) = (3, 11)\)
  • \((x_2, y_2) = (6, 9)\)

Substituting the values into the slope formula:

\[ m = \frac{9 - 11}{6 - 3} \]

Calculating the numerator and the denominator:

\[ m = \frac{-2}{3} \]

Thus, the slope of the line that passes through the points \((3, 11)\) and \((6, 9)\) is:

\[ \boxed{-\frac{2}{3}} \]