Question

what is the slope of this line?
(4, 4)
(4, 1)
options: \\(\frac{3}{4}\\), \\(-\frac{3}{4}\\), 0, undefined

Explanation:

Step1: Recall the 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 \((4, 1)\) and \((4, 4)\). So \( x_1 = 4 \), \( y_1 = 1 \), \( x_2 = 4 \), \( y_2 = 4 \).

Step3: Substitute into the slope formula

Substitute the values into the formula: \( m=\frac{4 - 1}{4 - 4}=\frac{3}{0} \). Division by zero is undefined, so the slope of a vertical line (where \( x \)-coordinates are the same) is undefined.

Answer:

undefined