identity line

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Image:KeynesianCross 3.png

In a 2-dimensional Cartesian coordinate system, with x representing the abscissa and y the ordinate, the identity line{{citation|title=Set Theory for the Working Mathematician|volume=39|series=London Mathematical Society Student Texts|first=Krzysztof|last=Ciesielski|publisher=Cambridge University Press|year=1997|isbn=9780521594653|page=13|url=https://books.google.com/books?id=tTEaMFvzhDAC&pg=PA13}}.{{citation|title=Principles of Medical Statistics|first=Alvan R.|last=Feinstein|publisher=CRC Press|year=2001|isbn=9781420035681|page=301|url=https://books.google.com/books?id=pQ-jRsoBi5YC&pg=PA301}}. or line of equality{{citation|title=Encyclopedia of statistical sciences: Update, Volume 1|first1=Samuel|last1=Kotz|first2=Campbell B.|last2=Read|first3=David L.|last3=Banks|publisher=Wiley|year=1997|isbn=9780471118367|page=[https://archive.org/details/encyclopediaofst0001unse/page/455 455]|url=https://archive.org/details/encyclopediaofst0001unse/page/455}}. is the y = x line. The line, sometimes called the 1:1 line, has a slope of 1.{{citation|title=Ecological Stoichiometry: The Biology of Elements from Molecules to the Biosphere|first1=Robert Warner|last1=Sterner|first2=James J.|last2=Elser|publisher=Princeton University Press|year=2002|isbn=9780691074917|page=16|url=https://books.google.com/books?id=53NTDvppdYUC&pg=PA16}}. When the abscissa and ordinate are on the same scale, the identity line forms a 45° angle with the abscissa, and is thus also, informally, called the 45° line.{{citation|title=Fundamental Engineering Mathematics: A Student-Friendly Workbook|first1=N.|last1=Challis|first2=H.|last2=Gretton|publisher=Elsevier|year=2008|isbn=9780857099396|page=38|url=https://books.google.com/books?id=RuiiAgAAQBAJ&pg=PA38}}. The line is often used as a reference in a 2-dimensional scatter plot comparing two sets of data expected to be identical under ideal conditions. When the corresponding data points from the two data sets are equal to each other, the corresponding scatters fall exactly on the identity line.{{citation|title=Handbook on Continuous Improvement Transformation: The Lean Six Sigma Framework and Systematic Methodology for Implementation|first1=Aristide|last1=van Aartsengel|first2=Selahattin|last2=Kurtoglu|publisher=Springer|year=2013|isbn=9783642359019|page=224|url=https://books.google.com/books?id=DUFEAAAAQBAJ&pg=PA224}}.

In economics, an identity line is used in the Keynesian cross diagram to identify equilibrium, as only on the identity line does aggregate demand equal aggregate supply.{{citation|title=Macroeconomic Theory: A Short Course|first=Thomas R.|last=Michl|publisher=M. E. Sharpe|year=2002|isbn=9780765611413|contribution=3.6 The Keynesian cross|pages=35–36|url=https://books.google.com/books?id=fPQKcV7ARqwC&pg=PA35}}.