Question

What is the slope of the line through the points (2/3,4/7) and (2/3,11/7)

Answer 1

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have:

$\left(\dfrac{2}{3},\ \dfrac{4}{7}\right)\to x_1=\dfrac{2}{3},\ y_1=\dfrac{4}{7}\\\\\left(\dfrac{2}{3},\ \dfrac{11}{7}\right)\to x_2=\dfrac{2}{3},\ y_2=\dfrac{11}{7}$

Substitute

$m=\dfrac{\dfrac{11}{7}-\dfrac{4}{7}}{\dfrac{2}{3}-\dfrac{2}{3}}=\dfrac{\dfrac{7}{7}}{0}\qquad\boxed{!!!!}$

Answer: The slope is not defined.