Question

which two points have an undefined slope?
a. (-1,1) and (1,-1)
b. (-2,2) and (2,2)
c. (-3,-3) and (-3,3)
d. (-4,-4) and (4,4)

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 \( x_2 - x_1 = 0 \) (vertical line), so \( x_1=x_2 \).

Step2: Check each option

• Option A: \( x_1=-1, x_2 = 1 \). \( x_2 - x_1=1-(-1)=2

eq0 \). Slope is defined.

• Option B: \( x_1=-2, x_2 = 2 \). \( x_2 - x_1=2-(-2)=4

eq0 \). Slope is defined.

• Option C: \( x_1=-3, x_2=-3 \). \( x_2 - x_1=-3-(-3)=0 \). Slope is undefined.
• Option D: \( x_1=-4, x_2 = 4 \). \( x_2 - x_1=4-(-4)=8

eq0 \). Slope is defined.

Answer:

C. \((-3, -3)\) and \((-3, 3)\)