Q: What is a line that a graph gets closer and closer to but does not touch?

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asymptote

the line goes down from left to right as the absolute value of the negative slope get bigger, the graph of the line gets steeper as the absolute value of the negative slope gets smaller, the graph of the line gets less steep ( apex )

less steep (apex)

Asymptote.

For a positive number, as the slope(y=mx+b where m is the slope) gets greater in value, the line gets steeper when plotted on a graph. For a negative number, as the slope(y=mx+b where m is the slope) gets greater in value, the line gets less steep when plotted on a graph.

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asymptote

As the slope gets bigger the graph becomes closer to vertical - from bottom left to top right.

There is nothing in the definition of "asymptote" that forbids a graph to cross its asymptote. The only requirement for a line to be an asymptote is that if one of the coordinates gets larger and larger, the graph gets closer and closer to the asymptote. The "closer and closer" part is defined via limits.

In geometry, an asymptote is a line that approaches the axis of a graph but does not touch or intersect. The line will continue to get closer but will never actually touch the axis. The line is said to be "asymptotic" if this occurs.

the line goes down from left to right as the absolute value of the negative slope get bigger, the graph of the line gets steeper as the absolute value of the negative slope gets smaller, the graph of the line gets less steep ( apex )

less steep (apex)

It gets steeper.

Asymptote.

asymptote

It gets longer Apex :)

A. As the absolute value of the negative slope gets bigger, the graph of the line gets steeper B. The line goes up from left to right C. As the absolute value of the negative slope gets smaller, the graph of the line gets less steep D. The line goes down from left to right E. The line shifts down

It gets closer to 0.