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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.
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.
Why are not all functions linear equations?
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
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.
What common characteristics do linear and nonlinear equations have?
Generally, both types of equation contain an equals sign and some combination of numbers and/or variables. That is the only thing I can think of that is common between all types of nonlinear and linear equations.
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.
Do all graphs of linear equations have x intercepts?
YES, all linear equations have x-intercepts. because of the x, y has to be there 2!
What does it mean for a system of linear equations to have no solutions?
It means that there is no set of values for the variables such that all the linear equations are simultaneously true.
