Let f(x) = ax + b, and
g(x) = cx + d, where a, b, c, and d, are any real
If f(x) and g(x) are graphed, what can you conclude about a, b, c, and/or
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?
The problem is asking us to
find the relationship between two different equations each with different variables.
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.
of the Problem
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.
two equations have to be opposite reciprocals (i.e. the numbers 2 and -1/2)
in order to be perpendicular.
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
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