What is the slope of the line that passes through the points left bracket, 2, comma, 8, right bracket(2,8) and left bracket, minus, 3, comma, 14, right bracket(−3,14)? 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 found using the formula:
\[m = \dfrac{y_2 - y_1}{x_2 - x_1}\]
In this case, the two points are (2,8) and (-3,14). Plugging in these values into the slope formula, we get:
\[m = \dfrac{14 - 8}{-3 - 2} = \dfrac{6}{-5} = -\dfrac{6}{5}\]
Therefore, the slope of the line passing through the two given points is \(-\dfrac{6}{5}\).