Question

What is the slope of the line that passes through the points left parenthesis, minus, 1, comma, 6, right parenthesis(−1,6) and left parenthesis, 14, comma, 3, right parenthesis(14,3)? Write your answer in simplest form.

Answer 1

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

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

In this case, the points are \((-1, 6)\) and \((14, 3)\). We can assign:

- \(x_1 = -1\)
- \(y_1 = 6\)
- \(x_2 = 14\)
- \(y_2 = 3\)

Now, we can plug these values into the slope formula:

\[
m = \frac{3 - 6}{14 - (-1)}
\]

Calculating the numerator and the denominator:

\[
m = \frac{3 - 6}{14 + 1} = \frac{-3}{15}
\]

Next, we simplify \(\frac{-3}{15}\):

\[
m = \frac{-1}{5}
\]

Thus, the slope of the line that passes through the points \((-1, 6)\) and \((14, 3)\) is

\[
\boxed{-\frac{1}{5}}
\]