Question: What is the slope of this line? \[ \begin{array}{c|c} x & y \\ \hline -5 & 2 \\ 5 & 0 \\…

What is the slope of this line?

\[ \begin{array}{c|c} x & y \\ \hline -5 & 2 \\ 5 & 0 \\ \end{array} \]

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Solution

To find the slope of the line, we can use the two given points: \((-5, 2)\) and \( (5, 0)\). The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substitute the given points \((-5, 2)\) and \( (5, 0)\) into the formula: \[ m = \frac{0 - 2}{5 - (-5)} \] Simplify the subtraction in the numerator and the denominator: \[ m = \frac{-2}{5 + 5} \] \[ m = \frac{-2}{10} \] Simplify the fraction: \[ m = \frac{-1}{5} \] The slope of the line is \( -\frac{1}{5} \).