The document discusses different forms and methods for graphing linear functions, including: 1) Standard, point-slope, and slope-intercept forms of linear equations. 2) Converting between these forms by solving for slope and y-intercept. 3) Graphing linear functions by finding the slope from two points using the point-slope form, making a table of x-y values, or finding the x- and y-intercepts. 4) Determining if two functions are parallel or perpendicular based on having equal or reciprocal slopes.

1. Linear Functions

2. Standard: Ax + By = CPoint Slope: y - y₁ = m(x-x₁)Slope-Intercept: y = mx + bSlope: m = 𝑦 −𝑦₁𝑥 −𝑥₁ Linear Function Expressions and Forms

3. Converting between FormsStandard to Slope-Intercept Ax + By = CBy = -Ax + Cy = −𝐴𝑥+𝐶𝐵y = −𝐴𝑥𝐵 + CLet −𝐴𝐵 = mLet C = by = mx + b Point-Slope to Slopey - y₁ = m( x - x₁)𝑦 −𝑦₁𝑥 −𝑥₁ = mm = 𝑦−𝑦₁𝑥−𝑥₁

4. Graphing Linear FunctionsUsing PointsUse two points ( x, y) and ( x₁, y₁)Find these points on the graphFor example:Let ( x, y) = ( 1, 2)and ( x₁, y₁) = ( 3, 4)

5. Graphing Linear FunctionsUsing pointsTo find SlopeCount 𝑹𝒊𝒔𝒆𝑹𝒖𝒏 on graph OrUse point-slope formY - y₁ = m( x - x₁)2 - 4 = m( 1 - 3)𝟐 −𝟒𝟏 −𝟑 = mm = −𝟐−𝟐m = 1Slope is 1

6. Graph 3y – 9x = 3First solve equation for y3y – 9x = 33y + 9x – 9x = 3 + 9x𝟏𝟑 ∙ 3y = 3 + 9x ∙ 𝟏𝟑y = 1 + 3xy = 3x + 1Equation is now in slope-intercept form Graphing Linear FunctionsMaking a Table

7. Graphing Linear FunctionsMaking a TableNow select some values for domainPlug values into y = 3x + 1

8. Graphing Linear FunctionsMaking a TableGraph ordered pairsDraw line through points

9. Graphing Linear FunctionsUsing interceptsFind x-intercept of 7x + y = -4Replace y with zero7x + 0 = -4𝟏𝟕 ∙ 7x + 0 = -4 ∙ 𝟏𝟕x = −𝟒𝟕 Find y-intercept of 7x + y = -4Replace x with zero7(0) + y = -4y = -4

10. Graphing Linear FunctionsUsing interceptsX-intercept is −𝟒𝟕Line intersects x-axis at ( −𝟒𝟕, 0)Y-intercept is -4Line intersects y-axis at ( 0, -4)

11. Find Equation of Function Using GraphsSlope-InterceptFind where line intersects y-axisThis value is bFind slope of line by 𝑹𝒊𝒔𝒆𝑹𝒖𝒏This value is my = mx + b

12. Find Equation of Function Using GraphsPoint-SlopePlug given point into ( x₁, y₁ )y – 2 = m( x – 3)Find slope by 𝑹𝒊𝒔𝒆𝑹𝒖𝒏 in graphPlug slope into my – 2 = 𝟏𝟐( x – 3)

13. Parallel Linear Functionsy = 𝟑𝟐 x + 1y = 𝟑𝟐 x + 4Are these functions parallel?Graph themThey are parallel

14. Perpendicular Linear Functionsy = −𝟑𝟒x + 2y = 𝟒𝟑 x + 3Are these functions perpendicular?Graph themThey are Perpendicular

15. Parallel and Perpendicular Linear FunctionsParallelFunctions with equal slopes are parallely = mx + by = 𝟑𝟐 x + 1y = 𝟑𝟐 x + 4m = 𝟑𝟐 PerpendicularFunctions with reciprocal slopes are perpendicularY = mx + bY = −𝟑𝟒 x + 2Y = 𝟒𝟑 x + 3M = −𝟑𝟒 and m = 𝟒𝟑

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