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VOCABULARY Coefficient – (Equation) Value multiplied by a variable (Table) Rate of Change (Graph) Slope ex. Y = 4x + 2 The coefficient is y = 7 - x The.

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Presentation on theme: "VOCABULARY Coefficient – (Equation) Value multiplied by a variable (Table) Rate of Change (Graph) Slope ex. Y = 4x + 2 The coefficient is y = 7 - x The."— Presentation transcript:

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2 VOCABULARY Coefficient – (Equation) Value multiplied by a variable (Table) Rate of Change (Graph) Slope ex. Y = 4x + 2 The coefficient is y = 7 - x The coefficient is 4 Constant Term – (Equation) Value NOT multiplied by a variable (Table) Value of y when x is zero (Graph) Y-Intercept ex. Y = 4x + 2 The constant term is y = 7 - x The constant term is 2 7 Coordinate Pair – (X, Y) Gives the point on a coordinate grid

3 VOCABULARY Coordinate Pair – (X, Y) Gives the point on a coordinate grid For example: (5, 3) Point of Origin – Point where x-axis and y-axis cross Point of Origin (0, 0)

4 VOCABULARY Y-Intercept – (Equation) Constant term (Table) Value of y when x is zero (Graph) Point where graphed line crosses y-axis Y-Intercept Point of Intersection – (Graph) Point where 2 (or more) graphed lines cross (Equation) Shared coordinate pair will solve both equations (Table) Common Data Point of Intersection

5 INVESTIGATION #1 Tips for a Good Graph Independent Variable vs. Dependent Variable (x - axis)(y - axis) Ask yourself, Which variable depends on the other? Labels - Title - Label Independent variable on x-axis (horizontal line) - Label Dependent variable on y-axis (vertical line) - Include units of measure - Include a key (if needed) - Scale: Increments need to be consistent and reasonable 4 Ways to Represent a Linear Relationship 1)Graph (Straight Line) 2)Table (Constant Rate of Change) 3)Equation (Form of y=mx+b) 4) Story Problem / Situation (2 variables – 1 depends on the other)

6 Slope: Y - intercept: 1 4 INVESTIGATION #2 Relating Tables, Graphs, and Equations Equation: y = 4x - 2 Coefficient: Constant Term: 4 -2 Table: x y Rate of Change: Value of y when x is zero: Graph: (0, - 2)

7 INVESTIGATION #2 cont. Symbolic form of a Linear Equation Y = mx + b Dependent Variable Y: m: X: b: Independent Variable (equation) Coefficient Constant Term (table) Rate of Change Value of y when x is zero (graph) Slope Y - Intercept Relationships The greater the coefficient- -the greater the Rate of Change -the steeper the slope If the coefficient is positive – -the y values in the table will increase -the slope will be positive If the coefficient is negative – -the y values in the table will decrease -the slope will be negative If the constant term is positive – -the line will cross above the point of origin If the constant term is negative – -the line will cross below the point of origin

8 INVESTIGATION #3 Introduction of the Graphing Calculator Review Calculator Tips & Trouble Shooting ( - ) vs. – key Window Settings X min: X max: X scl: Y min: Y max: Y scl: lowest value on the x-axis highest value on the x-axis lowest value on the y-axis highest value on the y-axis number of units each tick mark represents on the x-axis number of units each tick mark represents on the y-axis X min: X max: X scl: Y min: Y max: Y scl: Y = 4.7x + 78 Y = -1.3x (10, 125)

9 Point of Intersection INVESTIGATION #3 cont. Y = 4.7x + 78 Y = -1.3x Using the Table Enter both equations in the y = screen Press 2 nd graph to view the table Scroll up or down so that y values are getting closer together Search for Common Data where the y values are the same X Y1 Y Common Data (10,125) Using the Graph Enter both equations in the y = screen Press graph to view the graph Adjust window settings if needed to view the Point of Intersection Press 2 nd Trace to Calculate Select # 5 – Intersect Press enter 4 times (until P of I is shown at the base of the screen) Checking with the Equation Both equations should solve to be true statements when you substitute the values of the coordinate pair. Y = 4.7x = 4.7(10) = = 125 Y = -1.3x = -1.3(10) = = 125

10 INVESTIGATION #4 Parallel and Perpendicular Lines Parallel Parallel lines will never cross Equations with the same coefficient will have the same slope and will be parallel Example: Y = 3x + 8 Y = x Both lines have a slope of 3 Perpendicular Perpendicular lines cross at 90 degree angles The coefficients of the equations will be opposite reciprocals (+ / -)a/b b/a Example: Y = 3x + 8 Y = /3x Slope of 3 Slope of –1/3 3 and –1/3 are opposite reciprocals

11 INVESTIGATION #4 cont. SYMBOLIC METHOD Solving for y Y = 4x - 3 X = 12 Y = 4x – 3 Y = 4 (12) – 3 Y = 48 – 3 Y = 45 Solving for x y = -11 Y = 4x – = 4x – = 4x = x Eliminate the constant term Eliminate the coefficient Each line must contain an equal sign (only one) Each must contain the variable you are solving for

12 INVESTIGATION #5SLOPE Stair Step MethodCalculate Ratio Method Select 2 points on a graphed line Connect the points with a stair step Count the number of vertical units (rise) Count the number of horizontal units (run) Write the SLOPE as a ratio RISE RUN SLOPE = Reminder watch for negative slopes! 3 2 Rise is 3, run is 2 Negative slope Slope = (0, -2) Y = -1.5x - 2 Select 2 coordinate pairs from a graphed line Identify pair 1 and pair 2 Use the Slope formula SLOPE = y 1 – y 2 x 1 – x 2 (1,- 8) & (5,-16) – (-8) = = -2 x y Y = -2x - 6


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