I need help with 3 simple Pre-Calculous questions! (its actually the beginning of pre-cal so you only really need algebra knowledge)
1. Does every line have both an x-intercept and a y-intercept? Explain.
2. Does every line have an infinite number of lines that are parallel to the given line? Explain.
3. Does every line have an infinite number of lines that are perpendicular to the given line? Explain.
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I'm not 100% sure about the first one, but my guess would be "no." However I can't explain why because i'm not entirely sure.
I know for a fact the answer to the second one. That's so easy! but how do i explain something so simple!?
if you are talking about linear equations, every line will have an x- and y-int.
i think that there can infinite number of parallel lines to the given line.
and there might be an infinite number of perpendicular lines as well. you can make a perpendicular line anywhere in a line because it will go for an infinite space in both directions.
(i have never studied calculus before, but i am just using my prior knowledge.)
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Look at the drawing above.
Which lines have both x- and y-intercepts?
Which line has only an x-intercept?
Which line has only a y-intercept?
So the pictures with positive and negative slopes, both have an x and a y- intercept.
The picture with the slope as zero only has a y- intercept and the last one has just the x- intercept, right?
That cleared up the confusion in the first question! I just needed the visual
For the second question, it's soooo simple, I know. I fully understand that every line has an infinite number of lines that are parallel to it... I guess the issue is, I don't know how to express that verbally..
2. For any line in the form y = mx + b, there are an infinite number of constant values c for which you can change the y intercept (b) and replace it with c as long as you have the same slope.
3. For any line in the form y = mx + b, the same applies as long as you have a slope of -1/m
1. Every "line" as a y and x intercept, lines are infinitely distant in each direction. (Line segments are not infinitely distant)
The answer to 1 is "No."
Vertical lines have only an x-intercept.
Horizontal lines have only a y-intercept.
Only lines with a positive slope or negative slope have both an x-intercept and a y-intercept.
2. There is a concept of distance between parallel lines. It is the length of the segment that is perpendicular to both lines and has endpoints on the lines. That segment can have an infinite number of lengths, so there is an infinite number of parallel lines to any given line.
3. For a given line, there is a exactly one perpendicular line that passes through each point on the given line. Since there is an infinite number of points on the given line, there is an infinite number of perpendicular lines to the given line.