Question: What is the slope of this line? \[ \begin{array}{c|c} x & y \\ \hline -8 & -7 \\ -7 & -6…

What is the slope of this line?

\[ \begin{array}{c|c} x & y \\ \hline -8 & -7 \\ -7 & -6 \\ -6 & -5 \\ -5 & -4 \\ -4 & -3 \\ -3 & -2 \\ -2 & -1 \\ -1 & 0 \\ 0 & 1 \\ 1 & 2 \\ 2 & 3 \\ 3 & 4 \\ 4 & 5 \\ 5 & 6 \\ 6 & 7 \\ 7 & 8 \\ \end{array} \]

\[ (1, 4) \]

\[ (-2, -2) \]

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 formula for slope given 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 graph: \((-2, -2)\) and \((1, 4)\). Plug the points into the formula: \[ m = \frac{4 - (-2)}{1 - (-2)} \] Simplify the numerator and the denominator: \[ m = \frac{4 + 2}{1 + 2} \] \[ m = \frac{6}{3} \] Divide the numerator by the denominator: \[ m = 2 \] So, the slope of the line is \(2\).