Question

1. multiple choice which points are connected by a line with an undefined slope? a (-16, 8) and (-1, 10) b (-5, -15) and (18, 6) c (1, 1) and (-1, -1) d (-1, -4) and (-1, 15)

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). An undefined slope occurs when the denominator \( x_2 - x_1 = 0 \) (division by zero is undefined), meaning the \( x \)-coordinates of the two points are equal.

Step2: Check each option

• Option A: Points \((-16, 8)\) and \((-1, 10)\). \( x_2 - x_1=-1-(-16)=15

eq0 \), so slope is defined.

• Option B: Points \((-5, -15)\) and \((18, 6)\). \( x_2 - x_1 = 18-(-5)=23

eq0 \), slope is defined.

• Option C: Points \((1, 1)\) and \((-1, -1)\). \( x_2 - x_1=-1 - 1=-2

eq0 \), slope is defined.

• Option D: Points \((-1, -4)\) and \((-1, 15)\). \( x_2 - x_1=-1-(-1)=0 \), so slope is undefined.

Answer:

D. \((-1, -4)\) and \((-1, 15)\)