Question

what is the slope of this line?
the coordinate grid has a red vertical line passing through (-5, -1) and (-5, -3). the x-axis ranges from -8 to 8, and the y-axis ranges from -8 to 8. multiple choice options: 2/5, -2/5, 0, undefined

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the points

The two points on the line are \((-5, -1)\) and \((-5, -3)\). So, \( x_1=-5, y_1 = - 1, x_2=-5, y_2=-3 \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{-3 - (-1)}{-5 - (-5)}=\frac{-3 + 1}{-5 + 5}=\frac{-2}{0} \). Division by zero is undefined, so the slope of a vertical line (where \( x \)-coordinates are the same) is undefined.

Answer:

undefined