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the claim
A linear function is increasing if the slope m is greater than zero and decreasing if the slope m is less than zero.
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SUPPORTED
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5 sources for · 0 against
AS REPORTEDno primary record reached; this is what the reporting says
Is it true that a linear function is increasing if the slope m is greater than zero and decreasing if the slope m is less than zero?
Yes. Mathematical reference texts consistently state that linear functions with a slope greater than zero are increasing, while those with a slope less than zero are decreasing.
Verdict: SUPPORTED · 5 sources for, 0 against · Last checked
How claims like this are judged
Judged against reference works: claims of this kind are settled by reference works, not journal abstracts.
Evidence for · 5
Reference article covering this claim directly
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Wikipedia: Slope. (n.d.). Wikipedia. https://en.wikipedia.org/wiki/Slope
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More for · 4
Confirms a linear function is increasing if m > 0 and decreasing if m < 0.
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LibreTexts: LibreTexts: 10.4 Graphs of Equations. (n.d.). LibreTexts. https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT_206_Precalculus/10%3A_Appendix/10.4_Graphs_of_Equations
States an increasing function has a positive slope and a decreasing function has a negative slope.
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OpenStax: OpenStax Algebra and Trigonometry 2e: 4.1 Linear Functions. (n.d.). OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/f48a9644-4329-4387-9b38-4ac039f12570@
Explains that increasing linear functions have positive slopes and decreasing ones have negative slopes.
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LibreTexts: LibreTexts: 4.02%3A Linear Functions. (n.d.). LibreTexts. https://math.libretexts.org/Workbench/Algebra_and_Trigonometry_2e_(OpenStax)/04%3A_Linear_Functions/4.02%3A_Linear_Functions
Confirms increasing functions have positive slopes and decreasing functions have negative slopes.
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OpenStax: OpenStax College Algebra 2e: 4.1 Linear Functions. (n.d.). OpenStax. https://openstax.org/books/college-algebra-2e/pages/f48a9644-4329-4387-9b38-4ac039f12570@
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