How do you know if an equation is a linear equation?

A linear equation can be expressed as:

y = mx + b, where m is the slope and b is the y-intercept.

y = 12+2x, which can be rewritten as y = 2x + 12, is a linear equation with a slope of 2 and a y-intercept of 12.

To begin, both x and y should be to the first power (in other words, not have any exponents, such as x²) in order for the equation to be considered linear. One way to express a linear equation is simply " y = ax+b ", also known as slope-intercept form, where "a" is the slope of the line, and "b", being the constant term, is the y-intercept.

For your equation, y = 2x + 12, a=2, and 12=b.

You know it's a linear equation if the highest power is x^1, that is, x. y = mx +b is the form for a linear equation.

If highest power is x, then equation is linear

If " " x^2, then equation is quadratic

If x^3, then equation is cubic

etc.

an equation is said to be linear, if it has only powers of variables to either 1 or 0 (constant).

"A linear equation is an equation in which each term is either a constant or the product of a constant times the first power of a variable. "

A linear equation does not contain any variable to a power higher than the first power. your example has x and y to the first power and it is, therefor, a linear equation. If one of the powers is squared it would be quadratic if cubed a cubic etc.

It's any equation with (only) an x or a y in it as variables, usually of the form y=mx+b with b and m constants. The x and y refer to x- and y-coordinates on a graph

y=12+2x is an example of one, as is y=-x, 3=y-x, x=1.001+y

The highest power of any given variable is one. That is you don't have x^2, x^3, xy, etc. anywhere in the equation.

Linear equation has a form

ay = bx + c

where a, b and c are constants.

if it has the form

y=mx+b

y=4x+8

no powers OR xy term

e.g.

y = 2x -4