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Why does the line y = 5x have only one intercept instead of two?
AIts x-intercept and y-intercept coincide at the origin
BThe line never crosses either axis at any point
CThe line only exists within the first quadrant
DThe equation itself has no solutions at all
Answer & Solution
Correct answer: A. Its x-intercept and y-intercept coincide at the origin
1. Letting y = 0 gives 0 = 5x, so x = 0, and letting x = 0 gives y = 0, so both intercepts land on the same point.
2. Since the x-intercept and y-intercept are both (0, 0), the origin, the line effectively has only one intercept point instead of two distinct ones.
3. Because the x-intercept and y-intercept coincide, a third point is needed to graph the line accurately.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 4 "Graphs", section 4.3 Graph with Intercepts_
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