Intermath | Workshop Support

 Write-up

Title
Comparing Lines

Problem Statement
Let f(x) = ax + b, and g(x) = cx + d, where a, b, c, and d, are any real numbers.
If f(x) and g(x) are graphed, what can you conclude about a, b, c, and/or d, if:

a. f(x) and g(x) are parallel?
b. f(x) and g(x) are perpendicular?
c. f(x) does not cross the x-axis?
d. g(x) is horizontal?
e. f(x) and g(x) have the same y-intercept?

Investigation/Exploration of the Problem

Students can find the answers to the questions above by using the graphing calculator. Using trial and error students can discover the following:

a.       F(x) and g(x) are parallel when “a” and “c” are the same and “b” and “d” are different. This is true because lines that are parallel will have the same slope.

b.      F(x) and g(x) are perpendicular when “a” is equal to the opposite reciprocal of “c”.

c.       F(x) does not cross the x-axis when the line is horizontal and the y-intercept is not zero.

d.      G(x) is horizontal when the y coordinate is always the same. In order for this to happen the slope would need to be zero; thus the equation being y=b.

e.       F(x) and g(x) have the same y-intercept when “b” and “d” are the same.

Author & Contact
Dottie Mitcham