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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.
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.
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.
Why are linear equations called linear equations?
Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.
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 linear equations and functions different?
All linear equations are functions but not all functions are linear equations.
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.
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.
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
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.
Is linear algebra and linear equations the same?
Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.
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.
Why are linear equations called linear equations?
Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.
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).
