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?

Problem setup

The problem is asking us to find the relationship between two different equations each with different variables.

Plans to Solve/Investigate the Problem

My initial plan to solve the problem was to substitute values for the variables and manipulate the numbers in order to draw inferences.

Investigation/Exploration of the Problem

a.       Variables a and c have to be the same numbers in order for the two equations to be parallel, but we know that b is not equal to d.

b.      The two equations have to be opposite reciprocals (i.e. the numbers 2 and -1/2) in order to be perpendicular.

c.       In order for f(x) not to cross the x-axis, a has to be 0, and b can be any real number.  There must be no slope.

d.   If g(x) is horizontal, then c has to be 0 and d can be any real number.

e.   In order for f(x) and g(x) to have the same y-intercept, b and d have to be the same, causing the lines to intersect.  The slopes can vary.

Extensions of the Problem

None

Author & Contact
Mesha Rainey
mrainey@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials
None

U Important Note: You should compose your write-up targeting an audience in mind rather than just the instructor for the course.

You are creating a page to publish it on the web.