The document discusses different forms and methods for graphing linear functions, including: 1) The 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 = C Point Slope: y - y₁ = m(x-x₁) Slope-Intercept: y = mx + b Slope: m = 𝑦 −𝑦₁𝑥 −𝑥₁ Linear Function Expressions and Forms

3. Converting between Forms Standard to Slope-Intercept Ax + By = C By = -Ax + C y = −𝐴𝑥+𝐶𝐵 y = −𝐴𝑥𝐵 + C Let −𝐴𝐵 = m Let C = b y = mx + b Point-Slope to Slope y - y₁ = m( x - x₁) 𝑦 −𝑦₁𝑥 −𝑥₁ = m m = 𝑦−𝑦₁𝑥−𝑥₁

4. Graphing Linear FunctionsUsing 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)

5. Graphing Linear FunctionsUsing points To find Slope Count 𝑹𝒊𝒔𝒆𝑹𝒖𝒏 on graph Or Use point-slope form Y - y₁ = m( x - x₁) 2 - 4 = m( 1 - 3) 𝟐 −𝟒𝟏 −𝟑 = m m = −𝟐−𝟐 m = 1 Slope is 1

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

7. Graphing Linear FunctionsMaking a Table Now select some values for domain Plug values into y = 3x + 1

8. Graphing Linear FunctionsMaking a Table Graph ordered pairs Draw line through points

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

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

11. Find Equation of Function Using GraphsSlope-Intercept Find where line intersects y-axis This value is b Find slope of line by 𝑹𝒊𝒔𝒆𝑹𝒖𝒏 This value is m y = mx + b

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

13. Parallel Linear Functions y = 𝟑𝟐 x + 1 y = 𝟑𝟐 x + 4 Are these functions parallel? Graph them They are parallel

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

15. Parallel and Perpendicular Linear Functions Parallel Functions with equal slopes are parallel y = mx + b y = 𝟑𝟐 x + 1 y = 𝟑𝟐 x + 4 m = 𝟑𝟐 Perpendicular Functions with reciprocal slopes are perpendicular Y = mx + b Y = −𝟑𝟒 x + 2 Y = 𝟒𝟑 x + 3 M = −𝟑𝟒 and m = 𝟒𝟑

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