On Lines 

Vertical lines are not functions. They are included in this library for completeness.
So where does the equation x = "some constant" come from?
Check out the ordered pairs on the line x = 3.7. Every x value is 3.7. ANY y, which is used, is matched with the same x value, in this case 3.7, as are all the other y values.
Vertical lines have no slope since the x value never changes.
They often occur as vertical asymptotes for other functions. The reciprocal function has as an asymptote the vertical line x = 2. The reciprocal function has as an asymptote the vertical line x = 2. The reciprocal function has as a vertical asymptote the vertical line x = 4.
Horizontal lines are the graphs of constant functions, those whose values never change no matter what values are acted upon. Any x value produces the same y value as that of all the other x values: the result is constantly the same.
The slope of a horizontal line is zero.
They often occur as as the horizontal asymptotes for other functions. The reciprocal function has as an asymptote the horizontal line y = 0. The reciprocal function has as an asymptote the horizontal line y = 0. The reciprocal function has as a horizontal asymptote line y = 3.
Horizontal lines are polynomials of degree zero: y = a is also where the n, or degree, is zero.
The coefficient of the x term is the slope of the line, when the equation is written as an expression equal to y. The slope of y= 3x + 1 is 3 and of y = 4x + 8 is 4.
The yintercept is the constant term, when the equation is written as an expression equal to y. The yintercept of of y= 3x + 1 is 1 and of y = 4x + 8 is 8.
Linear functions are important.
Direct variation is described by a linear function: y = kx.
A linear regression line y = ax + b may be used to describe a relation statistically.
The equation 3x + 1 = 4x + 8 may be solved by graphing y = 4x + 8, y = 3x + 1, and noting that the xvalue of their intersection (1,4) is 1. The solution to the equation is 1.
This page is from Exploring Functions Throught the Use of Manipulatives (ISBN: 0962359335).
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