Different Forms of Linear Equations

Different Forms of Linear Equations

Slope Y-intercept Form, Point-Slope Form, Standard Form

Slope Y-intercept Form

• Y= mx + b

• of a line is: y=mx+b where m is the slope and b is the y-intercept. The y-intercept is always where the line intersects the y-axis, and will always appear as (0,b) in coordinate form.

Slope Intercept Form>Standard Form

• Subtract mx from both sides y - mx = (mx - mx ) + by - mx = b

• Subtract b from both sides (optional)y - mx - b = b - by - mx - b = 0

• Rearrange to put the x term first-mx + y - b = 0

• Let the fraction A/B represent m. If m is an integer, then B will equal 1.-A/Bx + y - b = 0

• Multiply both sides of the equation by the denominator B-Ax + By - Bb = 0

• Let Bb = C-Ax + By - C = 0

• Ax + By= C

Standard Form

• Standard Form:  Ax + By = CThis means  that we want the variables (x & y) to be on the left-hand side and the constant (6) to be on the right-hand side.When we move terms around, we do so exactly as we do when we solve equations!  So, remember... Whatever you do to one side of the equation, you must do to the other side!

Point-Slope Form

• Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).

Point-Slope Form > Slope intercept form

Point-Slope Form>Standard Form