Linear functions

Linear Functions

Standard: Ax + By = C

Point Slope: y - y₁ = m(x-x₁)

Slope-Intercept: y = mx + b

Slope: m =

Linear Function Expressions and Forms

Converting between Forms

Standard to Slope-Intercept

Ax + By = CBy = -Ax + Cy = y = + CLet = mLet C = by = mx + b

Point-Slope to Slope

y - y₁ = m( x - x₁)

= m

m =

Graphing Linear Functions

Using Points

Use two points ( x, y) and ( x₁, y₁)

Find these points on the graph

For example:Let ( x, y) = ( 1,

2)and ( x₁, y₁) = (

3, 4)

Graphing Linear FunctionsUsing points

To find Slope Count on graph

Or Use point-slope form Y - y₁ = m( x - x₁)

2 - 4 = m( 1 - 3) = mm = m = 1

Slope is 1

Graph 3y – 9x = 3 First solve equation for y

3y – 9x = 33y + 9x – 9x = 3 + 9x

∙ 3y = 3 + 9x ∙ y = 1 + 3xy = 3x + 1

Equation is now in slope-intercept form

Graphing Linear FunctionsMaking a Table


Now select some values for domain

Plug values into y = 3x + 1


Graph ordered pairs

Draw line through points

Graphing Linear FunctionsUsing intercepts

Find x-intercept of 7x + y = -4

Replace y with zero

7x + 0 = -4 ∙ 7x + 0 = -4 ∙

x =

Find y-intercept of 7x + y = -4

Replace x with zero

7(0) + y = -4y = -4

Graphing Linear FunctionsUsing intercepts

X-intercept is Line intersects x-

axis at ( , 0) Y-intercept is -4 Line intersects y-

axis at ( 0, -4)

Find Equation of Function Using Graphs

Slope-Intercept

Find where line intersects y-axis

This value is b Find slope of line

by This value is m y = mx + b

Find Equation of Function Using GraphsPoint-Slope

Plug given point into ( x₁, y₁ )y – 2 = m( x – 3)

Find slope by in graph

Plug slope into my – 2 = ( x – 3)

Parallel Linear Functions

y = x + 1 y = x + 4 Are these

functions parallel? Graph them They are parallel

Perpendicular Linear Functions

y = x + 2 y = x + 3 Are these

functions perpendicular?

Graph them They are

Perpendicular

Parallel and Perpendicular Linear Functions

Parallel Functions with

equal slopes are parallel

y = mx + by = x + 1y = x + 4

m =

Perpendicular Functions with

reciprocal slopes are perpendicular

Y = mx + bY = x + 2Y = x + 3 M = and m =

TI-Nspire CAS Student Software, All TI-Nspire CAS Calculator images, September 22, 2010, Copy Righted Texas Instruments.

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Linear functions