Intermath | Workshop Support


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?

Problem setup

During class, I have a basic (low level) understanding of the problem while class participants are talking about terminology, functions, and possible problem solutions. I have difficulty taking my basic knowledge and putting it into terms someone else might understand. I believe the problem should be set up to compare specified line functions and that a graphing calculator allows for visual understanding.


Plans to Solve/Investigate the Problem

Solved the problem by writing and graphing the equations (make a table, pick x values, find y, plot points.)


Investigation/Exploration of the Problem

a. a and c have to be equal for f(x) and g(x) to be parallel. b and d are different.

b. a=-1/c

c. It is a horizontal line if f(x) does not cross the x-axis. The slope is 0.

d. g(x) is vertical.

e. Yes f(x) and g(x) have the same y-intercept if b and d are same.


Extensions of the Problem

Additional practice using graphing calculator.

Author & Contact
Susan Kelly