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What is the key difference between the graphs of y = 4x and y = 4?
AIn y=4x, y stays constant; in y=4, y depends on x
BIn y=4x, y depends on x; in y=4, y stays constant
CBoth equations produce the exact same horizontal line
DBoth equations produce the exact same vertical line
Answer & Solution
Correct answer: B. In y=4x, y depends on x; in y=4, y stays constant
1. The equation y = 4x has two variables, so the value of y changes according to whatever value x takes.
2. The equation y = 4 has only one variable, so y is constant and does not depend on x at all.
3. As a result, y = 4x graphs as a slanted line through the origin, while y = 4 graphs as a horizontal line, so the two graphs are not the same.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 4 "Graphs", section 4.2 Graph Linear Equations in Two Variables_
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