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?

Expert Answers

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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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