Question

part 2 of 2
why can you not say that two vertical lines have equal slope? why can you not say that the product of the slopes of a vertical and horizontal line is - 1?
why can you not say that two vertical lines have equal slope?
a. vertical lines have undefined slope, and an undefined object has no value. two undefined quantities cannot be equal because they have no value.
b. every vertical line passes through the origin. this means that the slope between two points cannot be calculated for a vertical line. because of this, the slopes of vertical lines cannot be compared.
c. vertical lines have zero slope. two quantities that are both zero cannot be equal to each other because their quotient is undefined.
d. vertical lines have infinite slope, and infinity is not a number. two infinite quantities cannot be equal because they have no value.
why can you not say that the product of the slopes of a vertical and horizontal line is - 1?
a. horizontal lines have undefined slope. the product of an undefined quantity and any number is still undefined and cannot be equal to - 1.
b. vertical lines have undefined slope. the product of an undefined quantity and any number is still undefined and cannot be equal to - 1.
c. every vertical line passes through the origin. this means that the slope between two points cannot be calculated for a vertical line. because of this, the slopes of vertical lines cannot be multiplied.
d. vertical lines have infinite slope. the product of an infinite quantity and any number is infinite and cannot be equal to - 1.

Explanation:

La pendiente de una línea vertical está definida como $\frac{\Delta y}{\Delta x}$, donde $\Delta x = 0$ ya que las coordenadas $x$ de cualquier par de puntos en una línea vertical son iguales. Dividir entre cero es indefinido, por lo que la pendiente de una línea vertical es indefinido. Un objeto indefinido no tiene un valor real, y dos cantidades indefinidas no pueden ser iguales. Además, la pendiente de una línea horizontal es 0. El producto de una cantidad indefinida (la pendiente de una línea vertical) y cualquier número (en este caso, la pendiente de una línea horizontal que es 0) sigue siendo indefinido y no puede ser - 1.

Answer:

Why can you not say that two vertical lines have equal slope? A. Vertical lines have undefined slope, and an undefined object has no value. Two undefined quantities cannot be equal because they have no value.
Why can you not say that the product of the slopes of a vertical and horizontal line is - 1? B. Vertical lines have undefined slope. The product of an undefined quantity and any number is still undefined and cannot be equal to - 1.