A linear equation is one in which there is an actual slope. In other words, if you graph it, it'll be a straight line.
There are two ways of displaying a linear relationship:
General form: Ax + By + C = 0; A B and C are all real numbers (though it is generally simplified so that they can all be expressed as integers.)
Standard form: y = mx + b, where m and b are real numbers. This form is also called slope-intercept form.
If you're given an equation where y = xn, where n isn't 1, then that would not be linear, since the graph is not a straight line, whereas y = x is linear. If y = x is graphed, then you'll see that it's a perfectly straight line.
Since I rambled, I'll summarize: from the equation, you can tell if the relationship is linear if it can be expressed either as Ax + By + C = 0 or y = mx + b (A, B, C, m, b are all real numbers)
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A standard form of a linear equation would be: ax + by = c
No. It is an estimated equation that defines the best linear relationship between two variables (or their transforms). If the two variables, x and y were the coordinates of a circle, for example, any method for calculating the regression equation would fail hopelessly.
The question contains an expression, not an equation. An expression does not have a graph. Furthermore, even if it were an equation, its form suggests that it would be a linear equation and a linear equation does not open in any direction.
In general, it is very difficult. Even if a graph looks like a straight line over the domain there is no guarantee that the underlying equation makes the equation non-linear as you move away from the visible domain. A typical example, from school physics, concerns Hooke's law. The extension of a length of wire under different strains follows a linear relationship. Until the strain reaches a critical level and then the relationship goes all haywire. Looking at the graph below that critical level, the equation would be a straightforward linear one. But that is true only as far as it goes.
It is not. It is called a LINEAR equation. This is because the word linear refers to a line and, if the solutions of the equation, in the form of ordered pairs (x,y), were plotted on a Cartesian plane, they would all lie on a straight line.