a slope of unity

USAGE SUMMARY

The phrase "a slope of unity" is correct and usable in written English.
It can be used in mathematical or graphical contexts to describe a line or function that has a slope of one, indicating a direct proportionality between two variables. Example: "In the graph, the line representing the relationship between the two variables has a slope of unity, demonstrating that for every increase in one variable, the other increases by the same amount."

✓ Grammatically correct

Science

Mathematics

Data Analysis

Human-verified examples from authoritative sources

Exact Expressions

14 human-written examples

The blue line depicts a slope of unity.

Nature

Interestingly, the onset temperature of the endothermic peak linearly increased with a slope of unity against Ta and was observed at about 14 °C above Ta.

Polymer

A linear relation with a slope of unity between the apparent melting peak temperature, Tm, of the less perfect crystals and the crystallization temperature, Tc, is found, i.e. Tm (°C =Tc+5.1, at an extremely low level of crystallinity.

Polymer

The green line has a slope of unity (i.e., y=x).

Progress in Earth and Planetary Science

An ideal prediction should show a slope of unity (1), intercept of zero (0), and R2 = 1.

International Journal of Disaster Risk Science

If the ion exchange is the only controlling process of groundwater composition, the relation between (Ca2+ + Mg2+)–(SO4 2− + HCO3 −) and Na+ Cl− should show negative linear trend with a slope of unity, considering the participation of cations in the ion exchange reaction (Fisher and Mullican 1997).

Applied Water Science

Human-verified similar examples from authoritative sources

Similar Expressions

46 human-written examples

The expectation was a perfect correlation with a regression slope of unity.

Plosone

As body size increases, BMR in reptiles, birds, and mammals increases with a slope of less than unity, with an exponent of either 0.67 (White & Seymour, 2003, 2005) or of 0.75 (Brody, 1945; Savage et al., 2004) being found in the literature.

Biological Reviews

Equation 9 presents a straight line with slope of unity in a log log plot of RQI vs, φz.

Journal of Petroleum Exploration and Production Technology

Equation (8) presents a straight line with slope of unity in RQI vs φ z diagram.

Journal of Petroleum Exploration and Production Technology

The developed model in Eq. 13 above reveals that a log log plot of SN versus reservoir quality should develop a unit slope line describing a flow unit with unique slope of unity.

Journal of Petroleum Exploration and Production Technology

Expert writing Tips

Best practice

When describing graphs or data, use "a slope of unity" to clearly indicate a direct proportional relationship between the x and y axes. This is particularly useful in scientific and engineering contexts.

Common error

Avoid using "a slope of unity" interchangeably with a high correlation coefficient. While a slope of unity indicates a direct, proportional relationship, a high correlation only suggests a strong association, not necessarily a 1:1 correspondence.

Linguistic Context

The phrase "a slope of unity" functions as a descriptive term in mathematical and scientific contexts. It specifies the gradient of a line, indicating a direct proportional relationship between two variables. As confirmed by Ludwig, the phrase is grammatically correct and widely used.

Expression frequency: Common

Frequent in

Science

60%

Academia

20%

News & Media

10%

Less common in

Wiki

5%

Formal & Business

3%

Reference

2%

Ludwig's WRAP-UP

The phrase "a slope of unity" is a grammatically correct and commonly used term, particularly in scientific and technical fields, to describe a direct proportional relationship between two variables. Ludwig confirms its validity and provides numerous examples of its usage in context. When writing, remember that this phrase precisely describes the gradient of a line on a graph, indicating a 1:1 correspondence. Be careful not to confuse it with a general correlation, which doesn't necessarily imply direct proportionality. Alternative phrases include "unit slope" or "slope equal to one". By understanding its meaning and appropriate contexts, you can effectively use "a slope of unity" in your writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

Unit slope

Concise alternative using 'unit' as an adjective to describe the slope.

Slope equal to one

Directly states the value of the slope.

Unity gradient

Simple alternative with gradient.

Gradient of 1

A more concise way of specifying the steepness of the slope.

Directly proportional relationship

Focuses on the relationship implied by a slope of unity.

Linear relationship with a gradient of one

Uses 'gradient' as a synonym for slope and specifies linearity.

One-to-one correspondence

Highlights the direct mapping between variables.

Proportional increase

Emphasizes the proportional change between variables.

45-degree slope

Expresses slope in geometric terms.

Linear function with a coefficient of one

Describes the slope in terms of a linear function.

FAQs

How do I interpret "a slope of unity" in data analysis?

A slope of unity indicates a direct proportional relationship between two variables. For every unit increase in one variable, the other variable increases by one unit as well.

What does it mean if a regression line has "slope equal to one"?

It signifies that the change in the dependent variable is exactly the same as the change in the independent variable. This is a perfect linear and proportional relationship.

When is it appropriate to use the phrase "a slope of unity" in scientific writing?

Use this phrase when accurately describing graphical data or mathematical models where the relationship between variables is directly proportional and linear. Ensure your data supports this claim before using the phrase.

What's the difference between "direct proportionality" and "a slope of unity"?

"A slope of unity" refers to the graphical representation of direct proportionality. "Direct proportionality" is the mathematical relationship itself, while "a slope of unity" is how that relationship appears on a graph.