world 3-3 the 3 different forms of a linear equation
DESCRIPTION
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 aTRANSCRIPT
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