What is the slope of the line that passes through the points left bracket, minus, 6, comma, 8, right bracket(−6,8) and left bracket, minus, 9, comma, 7, right bracket(−9,7)? Write your answer in simplest form.
The slope of a line passing through two points, \((x_1, y_1)\) and \((x_2, y_2)\), can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, your first point is \((-6, 8)\), so \(x_1 = -6\) and \(y_1 = 8\). Your second point is \((-9, 7)\), so \(x_2 = -9\) and \(y_2 = 7\).
Plugging these values into the formula gives you:
\[ m = \frac{7 - 8}{-9 - (-6)} \]
\[ m = \frac{-1}{-9 + 6} \]
\[ m = \frac{-1}{-3} \]
\[ m = \frac{1}{3} \]
So, the slope of the line that passes through the points \((-6, 8)\) and \((-9, 7)\) is \(\frac{1}{3}\).