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 If a line has no y-intercept, what can you say about the line? What if a line has no...

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yissy | Student, College Freshman | Honors

Posted September 25, 2012 at 10:55 PM via web

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 If a line has no y-intercept, what can you say about the line? What if a line has no x-intercept?

Think of a real-life situation where a graph would have no x- or y-intercept. Will what you say about the line always be true in that situation?

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lfryerda | High School Teacher | (Level 2) Educator

Posted September 26, 2012 at 12:10 AM (Answer #1)

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If a line has no y-intercept, that means it never intersects the y-axis, so it must be parallel to the y-axis.  This means it is a vertical line, such as `x=3` .  This slope of this line is undefined.

If the line has no x-intercept, then it never intersects the x-axis, so it must be parallel to the x-axis.  This means it is a horizontal line, such as `y=-5` .  This slope of this line is zero.

A real-life situation of a line that has no y-intercept is the equation of a vertical wall.  This is a line such as x=5.  

A real-life situation of a line that has no x-intercept is the equation of a floor, such as the line y=10.

Lines that have no y-intercept are vertical lines that are parallel to the y-axis, such as the line x=10.  Lines that have no x-intercept are horizontal lines that are parallel to the x-axis, such as the line y=2.

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quantatanu | Student, Undergraduate | Valedictorian

Posted September 26, 2012 at 12:15 AM (Answer #2)

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If a line has no y-intercept, that means it never cuts y-axis and that is only possible when the line is parallel to y-axis. 

If the line has no x-intercept then the line is parallel to x-axis.

If a line does not have x or y intercept, that will mean that it is not possible in a 2 dimensional graph paper, we will need 3 dimensions. because  if a line does not have x or y intercep then it must be parallel to both x & y axes,  and so it must be parallel to the x-y plane and hence perpendicular to z-axis.

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