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 y-intercept is the constant term, when the equation is written as an expression equal to y. The y-intercept 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 x-value 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: 0-9623593-3-5).
You are hereby granted permission to make ONE printed copy of this page and its picture(s) for your PERSONAL and not-for-profit use. YOU MAY NOT MAKE ANY ADDITIONAL COPIES OF THIS PAGE, ITS PICTURE(S), ITS SOUND CLIP(S), OR ITS ANIMATED GIFS WITHOUT PERMISSION.
© 2006, 2019, 2020, Agnes Azzolino