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?
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:
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.
and g(x) are perpendicular when “a” is equal to the opposite
reciprocal of “c”.
does not cross the x-axis when the line is horizontal and the y-intercept
is not zero.
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.
and g(x) have the same y-intercept when “b” and “d”
are the same.
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