Respuesta :
However, it's impossible to divide by 0, so the slope of a vertical line is always undefined. Now consider the y-axis on a graph. The y-axis is the line x = 0, and it is a vertical line. Therefore, all vertical lines, which have undefined slopes, are parallel to the y-axis.
Vertical lines have undefined (or no) slope always, so this is a true statement.
To see why, look at a horizontal line (which is perpendicular). They have zero slope. That comes from the y = mx + b slope intercept form and their equation being y = b, and b is some number. Also, we use the idea that if two lines are perpendicular, the product of their slopes is -1; in other words, the slopes are negative reciprocals of one another.
Let's say the slope is [tex] \frac{0}4} [/tex]. If we wanted a horizontal line, which is perpendicular to a vertical line, we take the negative reciprocal of [tex] \frac{0}4} [/tex], which is [tex] \frac{-4}{0} [/tex]. That's undefined because we are dividing by zero. Try this for number and you'll always be dividing by zero, which is undefined.
The statement above, "Vertical lines always have an undefined slope", is TRUE.
