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.
21 - GRAPHS THE SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES.pptxbernadethvillanueva1
GRAPHS THE SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
GRAPHS THE SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
GRAPHS THE SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
GRAPHS THE SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
Factor Theorem and Remainder Theorem. Mathematics10 Project under Mrs. Marissa De Ocampo. Prepared by Danielle Diva, Ronalie Mejos, Rafael Vallejos and Mark Lenon Dacir of 10- Einstein. CNSTHS.
21 - GRAPHS THE SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES.pptxbernadethvillanueva1
GRAPHS THE SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
GRAPHS THE SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
GRAPHS THE SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
GRAPHS THE SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
Factor Theorem and Remainder Theorem. Mathematics10 Project under Mrs. Marissa De Ocampo. Prepared by Danielle Diva, Ronalie Mejos, Rafael Vallejos and Mark Lenon Dacir of 10- Einstein. CNSTHS.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
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
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