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Linear equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one or more variables. Linear equations occur with great regularity in applied mathematics.

If one equation has only one variable, it is said to be an equation in one variable or one unknown. There are equations having more than one unknown.

The greatest exponent of the variable in an equation in one unknown is called the degree of the equation.

An equation in which the greatest exponent of the variable after simplification is one, is called a linear equation. Thus, the degree of a linear equation is one.

General form of a linear equation

A linear equation in one unknown can be written as:

ax + b = 0 where a and b are real numbers and a≠ 0.

The value (or values) of the variable (or variables) which make the equation a true statement is (are) called solution(s) of the equation.

• A solution is also called a root of the equation.
• A linear equation in one variable has only one solution.

Slope- intercept form

There are many standard forms of equations for straight lines. Among these the most useful form of straight-line equations is the slope-intercept form: y = mx + b

This is called the slope-intercept form because m is the slope and b gives the y-intercept.. It is in the form y=, which makes it easiest to plug into, either for graphing or doing word problems. Just plug in your x-value; the equation is already solved for y. Also, this is the only format you can plug into your graphing calculator; you have to have a y= format to use a graphing utility. But the best part about the slope-intercept form is that you can read off the slope and the intercept right from the equation. This is great for graphing, and can be quite useful for word problems.

The slope-intercept form is an extremely useful special case of the point-slope form of the equation defining a straight line. It is written as y = mx + b, where m is the slope and b is the y-intercept, the point where the line intersects the y-axis. The x- and y-intercepts of a line are the points where the line intersects the x- and y-axis, respectively.

Some equations will already be in the slope/intercept form. In that case, there is no need to rewrite it. However, if it isn't in that form, then we need to rewrite it. Basically, to get it into the slope/intercept form, we solve the linear equation for y.

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