Respuesta :
Answer:
No, it is not possible
Step-by-step explanation:
Required
Is it possible to have a line segment with: [tex]m = \infty[/tex]
To answer this question, we will interpret the steepness as slope.
So, we have:
[tex]m = \infty[/tex]
The interpretation of a line with: [tex]m = \infty[/tex] is:
It starts from (x,y_1) and ends at (x,y_2)
When the slope (m) is then calculated, we have:
[tex]m = \frac{y_2 - y_1}{x_1 - x_1}[/tex]
[tex]m = \frac{y_2 - y_1}{0}[/tex]
[tex]m = \infty[/tex]
What this means is that, the line has no end points.
A line segment as described here means a line that has endpoints (i.e. a finite starting point and a finite finish point)
So, we've established that: [tex]m = \infty[/tex] means no endpoints and a line segment has end points, then we can conclude that it is not possible to create a line segment with [tex]m = \infty[/tex]
Steepness of a line is the rise or fall of it at a sharp angle.The Is it not possible to create a line segment with infinite steepness, as the slope of the such line will be infinite whether a line is plotted with finite points.
Steepness-
Steepness of a line is the rise or fall of it at a sharp angle. The slope of the line describe the steepness of a line.
Infinite steepness-
A infinite steepness refers to a vertical line on the graph. When the line with infinite steepness plotted on the graph it is only parallel to the y axis. The change on the x axis is zero and does not move in the x axis, when a line has infinite steepness.
To understand it better suppose a line is passed through the point [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] points. For such line the slope of the line can be given as,
[tex]m=\dfrac{y_2-y_1}{x_2-x_1} [/tex]
The line with infinite steepness does not move in the x axis. The coordinate of the x axis same for the line. Thus,
[tex]x_2=x_1[/tex]
The slope for such line is,
[tex]m=\dfrac{y_2-y_1}{x_1-x_1} [/tex]
[tex]m=\dfrac{y_2-y_1}{0} [/tex]
[tex]m=\infty[/tex]
Thus the slope of the line is infinite. But the line With no finite point is not possible to plot.
Hence the Is it not possible to create a line segment with "infinite steepness, as the slope of the such line will be infinite whether a line is plotted with finite points.
Learn more about the steepness of the line here;
https://brainly.com/question/806542
