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How do you solve linear equations?i

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Linear equations have two variables, so there is not one solution to them.  Instead, there are an infinite number of ordered pairs that satisfy the equation.  These solutions are represented by a line.

The most common method of graphing a line is to convert it to slope-intercept form.  To do this, solve the equation for the variable y.  The equation will be in the form: y = mx + b.

In order to graph the line from the slope intercept form, plot a point at (0,b), which is known as the y-intercept.

Once the first point is found, a second point can be found using the slope (m).

If the number is a fraction, the top number tells you how many places to go up or down and the bottom number tells you how many places to go to the right.  If the number is a whole number, then it is the number of places to go up or down, while 1 is the number of places to go to the right.

If the number that is multiplied by x is positive, you will go up to the right.  If it is negative, you will go down to the right.

Once you have two points plotted, you can draw a straight line through them.  This line represents all of the possible solutions to the linear equation.

 

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