* Creation of Linear Functions from Slope and Y Intercept *

Euclidean Geometry states that Two Points determine a Line

therefore given two points in a Rectangular Coordinate System

a Linear Function can be created with one specific equation.

The Standard Form for a Linear Function is: Ax + By = C

The Slope Intercept Form for a Linear Function is: y = mx + b

The Slope, which is defined as the Rise / Run, can be determined by

the difference of the Y values over the difference of the X values.

Given two points (ordered pairs) in a Rectangular Coordinate System.

Therefore Slope is defined as follows: m = ( Y₂ – Y₁ ) / (X₂ – X₁)

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Given: Slope = -2/3 & P₁ = ( 0 , -2 ) Determine equation of a Linear Function

Substitute the Slope and the Y intercept into the Slope Intercept Form.

After all calculations are finished change into Standard Form.

y = ( -2/3 ) x + -2 +3y = -2x -2 +2x +3y = -2

Therefore the Linear Function for the given two points: +2x +3y = -2

Check by determing the X and Y intercepts.

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Given: Slope = +2/5 and P₁ = ( 0 , +3 ) Determine equation of a Linear Function

Substitute the Slope and the Y intercept into the Slope Intercept Form.

After all calculations are finished change into Standard Form.

y = ( +2/5 ) x + 3 +5y = +2x +3 -2x +5y = +3

Therefore the Linear Function for the given two points: -2x +5y = +3

Check by determing the X and Y intercepts.

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