Are all linear equations functions. I'd say yes. Because both contain domain and range. But..not all are graphed linear.
when is a linear equation not a function?
The exception is when the function represents a vertical straight line such as x = 8
A linear equation is a type of equation that represents a straight line when graphed on a coordinate plane. It contains two variables, typically represented as x and y, and can be written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Now, to answer your question, not all linear equations are functions. A function is a mathematical relationship where each input value (x) corresponds to exactly one output value (y). In other words, for every x-value, there should be a unique y-value. If this condition is not met, then the equation does not represent a function.
There are two main cases where a linear equation is not a function:
1. Vertical Line: If the linear equation has a slope of zero (m = 0), the resulting line will be a vertical line. A vertical line has a constant x-value but can have multiple y-values. Therefore, it fails the requirement of a function.
2. Repeated x-values: If two or more different x-values produce the same y-value, then the equation does not represent a function. In the case of a linear equation, this happens when the slope (m) is zero. For example, the equation y = 2 represents a horizontal line where all x-values will have the same y-value. Thus, it also fails the requirement of a function.
In summary, while linear equations generally represent functions, there are cases where they do not. A vertical line (m = 0) or a line with repeated x-values are examples of when a linear equation is not a function.