What is the slope of the line that passes through the points left bracket, minus, 1, comma, 6, right bracket(−1,6) and left bracket, 14, comma, 3, right bracket(14,3)? Write your answer in simplest form.
Answer
To find the slope of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the slope formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
For the points (-1, 6) and (14, 3), let's plug them into the formula:
\[ \text{slope} = \frac{3 - 6}{14 - (-1)} \]
\[ \text{slope} = \frac{-3}{14 + 1} \]
\[ \text{slope} = \frac{-3}{15} \]
In simplest form, this fraction can be reduced by dividing the numerator and the denominator by their greatest common divisor, which is 3:
\[ \text{slope} = \frac{-3 \div 3}{15 \div 3} \]
\[ \text{slope} = \frac{-1}{5} \]
So the slope of the line that passes through the points (-1,6) and (14,3) is \(-\frac{1}{5}\).