What is the slope of the line that passes through the points left bracket, minus, 1, comma, minus, 7, right bracket(−1,−7) and left bracket, 1, comma, minus, 13, right bracket(1,−13)? Write your answer in simplest form.
Answer
The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the slope formula:
\( m = \frac{y_2 - y_1}{x_2 - x_1} \),
where \( m \) is the slope of the line.
Given the two points \((-1, -7)\) and \((1, -13)\), we can label them as follows:
\( x_1 = -1, y_1 = -7, x_2 = 1, y_2 = -13 \).
Now we can plug these values into the formula:
\( m = \frac{-13 - (-7)}{1 - (-1)} \),
\( m = \frac{-13 + 7}{1 + 1} \),
\( m = \frac{-6}{2} \),
\( m = -3 \).
So, the slope of the line that passes through the points \((-1, -7)\) and \((1, -13)\) is \(-3\).