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A line with no slope is a vertical line;
i.e. a line that has a slope of 0, is simply a horizontal line. Mathematically, a line with zero slope corresponds to an equation like y = C, where C is just some constant number like 2, 80, or 1,000,000. If you think about it, since the variable, x, isn't in the above equation, y will equal that constant number, C, for every value of x. So, on a graph, if y is the same number for every position on the x-axis, it's a horizontal line.
A non-mathematical analogue is flat ground. If you're walking on a horizontal surface, like flat ground, you're not going upwards or downwards in elevation, therefore the ground has a zero slope.
The slope of a line is just a number which equals to the tangent of the angle that a line forms with the positive part of the x-axis. Since any vertical line form a 90 degree angle with the x-axis, and tan 90 degrees is undefined, then we say that a vertical line has no slope.
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What happens to the equation of the line as you change its slope?
The coefficient of x changes as the slope changes.
What happens to the slope when a line with positive slope gets close to vertical?
it gets larger
What happens to a line when the slope is negative?
it goes down
What happens to the line when the slope changes?
The angle that the line makes with the axes changes.
What happens to a line when the slope is a smaller and smaller?
As the slope gets smaller and smaller the line gets flatter and flatter (or more horizontal).
What happens to the line and its slope if you zoom in or out?
The slope of a line doesn't change if you zoom in or out.
What happens when you try to calculate the slope of a vertical line?
You cannot: the slope is not defined.
What happens to the equation of the line as you change its slope?
The coefficient of x changes as the slope changes.
What happens to the slope when a line with positive slope gets close to vertical?
it gets larger
What happens to a line when the slope is negative?
it goes down
What happens to the line when the slope changes?
The angle that the line makes with the axes changes.
What is the slope of the line defined by the equation y equal 8?
it doesnt slope, but goes constantly horizontal 8 squares up
What happens to a line when the slope is a smaller and smaller?
As the slope gets smaller and smaller the line gets flatter and flatter (or more horizontal).
What happens when the slope is 3 over 0?
When the slope is 3 over 0, it indicates a vertical line. In mathematical terms, a slope of 3 over 0 is considered undefined because division by zero is undefined in mathematics. This means that the line is vertical and does not have a defined slope in the traditional sense. The equation of a vertical line can be represented as x = a, where 'a' is the x-coordinate of any point on the line.
What happens to a line as the slope approaches 0?
It Gets Flatter!
What happens to a line as its slope is incrementally decreased from one to zero?
It approaches a horizontal line
What happens to a line as the slope approches 0?
The line becomes more and more level (horizontal).
