What is the slope of the line that passes through the points left bracket, minus, 9, comma, minus, 5, right bracket(−9,−5) and left bracket, minus, 1, comma, minus, 9, right bracket(−1,−9)? Write your answer in simplest form.
To find the slope of a line passing through two points, we use the formula:
\(\text{Slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}\)
Applying this formula to the given points (-9,-5) and (-1,-9), we have:
\(\text{Slope} = \frac{{-9 - (-5)}}{{-1 - (-9)}}\)
Simplifying this expression, we get:
\(\text{Slope} = \frac{{-9 + 5}}{{-1 + 9}} = \frac{{-4}}{{8}}\)
To express this slope in simplest form, we can divide both the numerator and the denominator by their greatest common divisor, which is 4:
\(\text{Slope} = \frac{{-4}}{{8}} = \frac{{-1}}{{2}}\)
Therefore, the slope of the line passing through the points (-9,-5) and (-1,-9) is \(\frac{{-1}}{{2}}\).