Question: What is the slope of this line? \[ \begin{array}{c|c} \text{Simplify your answer and write it…

What is the slope of this line?

\[ \begin{array}{c|c} \text{Simplify your answer and write it as a proper fraction, improper fraction, or integer.} \\ \hline \text{Answer:} & \boxed{\phantom{\frac{1}{2}}} \\ \end{array} \]

\[ \begin{array}{c|c} \text{Graph:} & \text{A line passing through the points (1, 3) and (-5, -5).} \\ \hline \text{Points:} & (1, 3), (-5, -5) \\ \end{array} \]

Solution

To find the slope of the line, use the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Identify the points on the line: \((-5, -1)\) and \((1, 3)\). Substitute the points into the formula: \[ m = \frac{3 - (-1)}{1 - (-5)} \] Simplify the expression: \[ m = \frac{3 + 1}{1 + 5} \] \[ m = \frac{4}{6} \] Simplify the fraction: \[ m = \frac{2}{3} \] The slope of the line is \(\frac{2}{3}\).