• 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

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