World 3-3The 3 Different Forms of a Linear Equation

Recall that there are 3 commonly used forms of quadratic functions; general,

and factored form.standard,Each tell us something different about the parabola.

Similarly there are 3 useful forms of linear functions.

1. Functional 2. General 3. Symmetric

y = ax + b ax + by + c = 0

1. Functional y = ax + b

Key Features• shows the slope, a = (Rise/Run) • shows the y-intercept b • can be graphed quickly (slope intercept method)• input x output y for a quick Table of Values• shows how y is dependant on x.

(0,b)

rise

run

a

y = -3x - 2

4y = -6x - 8

2SAME LINE!

2. General ax + by + c = 0

Key Features• no fractions or decimals and the RS must equal = 0• useful for solving systems of equations (Matrix)• shows co-linear lines (same line)

3x + 2y + 4 = 0 -3x -3x 2y + 4 = -3x

- 4 - 4 2y = -3x - 4

2 2 y = -3x - 2

2

6x + 4y + 8 = 0 -6x -6x 4y + 8 = -6x

- 8 - 8

4 4

3. Symmetric

Key Features• right side must equal 1• allows for quick graphing of intercepts• x intercept is a, y intercept is b

Graph using intercepts

Find the equation in all 3 forms passing through (2,4) and (-3,6)

Functional y=ax + b General ax+by+c = 0

Symmetric

Homework

World 3-3 Handout