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Linear equations can be written as y = mx + b. Any other function would be non-linear. Some linear equations are: y = 3x y = 2 y = -2x + 4 y = 3/4x - 0.3 Some non-linear functions are: f(x) = x2 y = sqrt(x) f(x) = x3 + x2 - 2
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What similarities and differences do you see between the function and linear equations?
Linear equations are a tiny subset of functions. Linear equations are simple, continuous functions.
Are all linear equations functions?
yes yes No, vertical lines are not functions
How can you determine if a linear equation is a function?
If we are talking about a linear equation in the form y = mx + b, then all linear equations are functions. Functions have at most one y value to every x value (there may be more than one x value to every y value, and some x- and y-values may not be assigned at all); all linear equations satisfy this condition.Moreover, linear equations with m ≠ 0 are invertible functions as well, which means that there is at most one x-value to every y-value (as well as vice versa).
What are the linear systems?
A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
Are linear equations and functions different?
All linear equations are functions but not all functions are linear equations.
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
Are all linear equations functions Is there an instance when a linear equation is not a function?
Linear equations are always functions.
How are functions like linear equations?
Most functions are not like linear equations.
How are functions and linear equations similar?
Linear equations are a small minority of functions.
What similarities and differences do you see between the function and linear equations?
Linear equations are a tiny subset of functions. Linear equations are simple, continuous functions.
Are all linear equations functions?
yes yes No, vertical lines are not functions
How are linear equations similar or different from functions?
A linear equation is a specific type of function that represents a straight line on a graph. While all linear equations are functions, not all functions are linear equations. Functions can take many forms, including non-linear ones that do not result in a straight line on a graph. Linear equations, on the other hand, follow a specific form (y = mx + b) where the x variable has a coefficient and the equation represents a straight line.
How are linear equations and functions alike and how are they different?
A linear equation is a special type of function. The majority of functions are not linear.
What do all functions that are not linear equations have in common?
They all have in common ranges or outcomes with more than one possibility.
How can you determine if a linear equation is a function?
If we are talking about a linear equation in the form y = mx + b, then all linear equations are functions. Functions have at most one y value to every x value (there may be more than one x value to every y value, and some x- and y-values may not be assigned at all); all linear equations satisfy this condition.Moreover, linear equations with m ≠ 0 are invertible functions as well, which means that there is at most one x-value to every y-value (as well as vice versa).
What similarities and differences do you see between functions and linear equations studied in Ch 3 Are all linear equations functions Is there an instance in which a linear equation is not a funct?
Assuming you work with two variables (like x and y) only: if the graph is a vertical line, e.g. x = 5, then it is not a function. Otherwise it is.
