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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

This problem asks you to figure out the relationship between different variables when they are used in two different equations.

 

Plans to Solve/Investigate the Problem

I plan to solve this problem by looking at the graphs of each equation and the concepts I have learned.

 

Investigation/Exploration of the Problem

 

a.       When f(x) and g(x) are parallel  you know that a and c are the same.  This is because in the equation y=mx+b, m is the slope.  Variables a and c are both in the slope position, so they must be equal.  Variable b and d are not equal. 

b.      When f(x) and g(x) are perpendicular, a and c are going to be opposite reciprocals of each other.

c.       If f(x) does not cross the x-axis, it is a horizontal line.  If a line is horizontal then its slope is zero.  Therefore, a is equal to zero and b and d can be anything except 0.

d.      If g(x) does not cross the x-axis, it is a horizontal line.  If a line is horizontal then its slope is zero.  Therefore, c is equal to zero.

e.       If f(x) and g(x) have the same y-intercept, b and d are the same.  This is because in the equation y=mx+b, b represents the y intercept which occurs when x = 0

Author & Contact
Benjamin Moore

My Email

Link(s) to resources, references, lesson plans, and/or other materials
Dr. Math
MathWorld

 

 

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