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