- Science Terms
- Parameter vs. Statistic
- Reoccurring vs. Recurring
- Linear vs. Nonlinear
- Observational Study vs. Experiment
- Histogram vs. Bar Graph
- Discrete vs. Continuous
- Validity vs. Reliability
- Type 1 vs. Type 2 Error
- Objective vs. Subjective Data
- Prospective vs. Retrospective Study
- Sample vs. Population
- Interpolation vs. Extrapolation
- Exogenous vs. Endogenous
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In math classes, we learn about different types of equations that can help us in our everyday life. Linear and non-linear equations are statements used for varying statistical procedures which produce different results. Depending on your career, you may use linear or nonlinear equations to understand certain data points.
Mathematical equations are utilized in a variety of different careers. These algebraic processes are used to determine unknown values. Users replace values in these equations with variables in order to represent correct solutions. These equations can be used in graphing or simply by solving to determine patterns.
Key Takeaways:
| Linear Equations | Nonlinear Equations |
|---|---|
| Linear equations are defined as equations that have a maximum of one degree. | Nonlinear equations are defined as equations that have a maximum degree of 2 or more than 2. |
| A linear equation forms a straight line or represents the equation for a straight line. | A nonlinear equation does not form a straight line when graphed. Instead, it forms a curve. |
| The representation for a linear equation is y=mx+c | The representation of a nonlinear equation is ax2+by2=c |
What Is a Linear Equation?
A linear equation is an equation that appears as a straight line on a graph. If the differences in the equation output are consistent when you use unknown variables, then the equation is considered linear. These equations have only one degree or a maximum of one degree.
The most common form of a linear equation can be explained by the form y = a + bx, where a and b both represent constants in the equations, where there are two variables present. This is the backbone of the linear equation. When plotted on graph paper, the equation forms a straight line with the line passing through the origin.
In physics and mathematics, linear equations are considered to be simple by professionals, but they are incredibly useful for both professional and personal settings. Some instances where linear equations can be used are;
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Variable costs. Linear equations are used to determine variable costs, such as a service. For example, if you have a professional install a fence and they charge $200 for the day and $0.50 for each yard of fencing, you can use the linear equation y=0.50x+200 to determine how much the service costs, where x represents each yard.
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Calculating rates. Linear equations can be used to determine rates in a certain scenario. For example, if you hire a bartender for an event and they charge $50 an hour where the event lasts six hours, you can use the equation y=50(6) to determine the overall price for your bartender.
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Earnings. Linear equations can determine earnings. For example, if a performer attends a show where the venue pays $1000 as well as $10 for each ticket processed, you can use the equation y=10x+1000, where y represents the earnings and x represents the number of tickets sold. This equation determines the overall earnings.
What Is a Nonlinear Equation?
A nonlinear equation is an equation that demonstrates itself as a curved line on a graph. This means the differences between the outputs of the equation are inconsistent when unknown variables are used. Nonlinear equations are not just curves, however. Nonlinear equations can take many forms but never a straight line as they do not appear in powers of one.
Nonlinear equations have the degree as 2 or more than 2, but never less than two. When the value of the degree is increased, the curvature of the graph will increase as well. The most common representation of a nonlinear equation is ax2+by2=c, where both x and y are variables and a,b, and c are constant values.
Nonlinear equations are more often used in professional settings than linear equations as these types of equations are typically very useful for project management activities or for making projections. They can be used for the following.
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Regression analysis. This statistical technique is used to understand which variable has an impact on a specific topic of interest. This analysis allows you to determine which factors matter most, which factors can be ignored, and how the factors may influence each other. The formula to use is y1=a+bx
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Logarithmic scales. This nonlinear scale is used most commonly when analyzing a large range of quantities. They’re especially useful when the data you’re looking at is much less or more than the rest of the data or when percentage differences between values are significant. An example of this equation is y=log10(x)
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S-curve. S-curve graphs are used in project management to illustrate the appropriate cumulative data for a specific task. For example, this data can be things like man hours plotted against time. S(x) = (1/(1+exp(-kx))^a is a simple equation, where the minimum value is 0, the maximum value is 1, k and a both >0 and control the shape.
Linear vs. Nonlinear FAQ
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What is the difference between nonlinear and linear equations?
Linear equations represent a straight line in a graph, whereas nonlinear equations are used to represent curves.
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When graphing linear and nonlinear equations, how do they look?
In a graph, a linear equation is a constant slope. The nonlinear equation has variations in the slope at different points.
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How do I determine if an equation is a linear or nonlinear equation?
To determine if an equation is a linear or nonlinear equation, determine the format of the equation. Take the equation y = 2x + 1, where the equation has the highest degree as one. This is a linear equation, and a nonlinear equation will not match this equation.
- Science Terms
- Parameter vs. Statistic
- Reoccurring vs. Recurring
- Linear vs. Nonlinear
- Observational Study vs. Experiment
- Histogram vs. Bar Graph
- Discrete vs. Continuous
- Validity vs. Reliability
- Type 1 vs. Type 2 Error
- Objective vs. Subjective Data
- Prospective vs. Retrospective Study
- Sample vs. Population
- Interpolation vs. Extrapolation
- Exogenous vs. Endogenous
Author
Caitlin Mazur is a freelance writer at Zippia. Caitlin is passionate about helping Zippia’s readers land the jobs of their dreams by offering content that discusses job-seeking advice based on experience and extensive research. Caitlin holds a degree in English from Saint Joseph’s University in Philadelphia, PA.
