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• Merry Havens

# Solving Linear Equations

Linear equations come in many forms. Easy conversion between the different forms can come in very useful for solving linear equations and graphing.

Slope Intercept form: y = mx + b where m is the slope and b is the y-intercept

most useful for graphing, i.e. y = 3 x +4....plot the

y-intercept first (0, 4) and then use the slope to

plot the next point (3 is the slope...always think of

it as a fraction...3/1....so, go up 3 from 0,4, then over 1

Now you have 2 points (0,4) and (1,7), make a line!

Standard form: Ax + By = C where A, B and C are whole numbers. If you wanted to

convert Standard Form to Slope Intercept Form, you

have to get y by itself on the left side. For example:

3 x + 6 y = 12 ...first subtract 3x from both sides (to

"move" it to the right side: 3x - 3x + 6 y = - 3 x + 12

simplify: 6 y = -3 x + 12 . . . we're getting closer. To

get y by itself, we have to divide (BOTH SIDES) by 6:

6y/6 = - 3 x/6 + 12/6 simplifies to y = -1/2 x + 2

Where the y-intercept is clear (2) and the slope is -1/2