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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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What is standard form linear equation's?
A standard form of a linear equation would be: ax + by = c
Is the regression equation a mathematical equation that defines the relationship between two variables?
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.
Which direction would the graph of y-x plus 2 plus 3 open?
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.
How do you find an equation from a graph?
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.
Why is y equals ax plus b called the linear equation?
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.
