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Linear Functions

Linear Functions. Chapter 5. 5.1 Rate of Change and Slope. Pg. 294 – 300 Obj : Learn how to find the rate of change from tables and find slope. Standards: F.LE.1.b and F.IF.6. 5.1 Rate of Change and Slope. Rate of Change – shows the relationship between two changing quantities Slope.

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Linear Functions

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  1. Linear Functions Chapter 5

  2. 5.1 Rate of Change and Slope • Pg. 294 – 300 • Obj: Learn how to find the rate of change from tables and find slope. • Standards: F.LE.1.b and F.IF.6

  3. 5.1 Rate of Change and Slope • Rate of Change – shows the relationship between two changing quantities • Slope

  4. 5.1 Rate of Change and Slope • Types of Slope • Positive • Negative • Zero • Undefined

  5. 5.2 Direct Variation • Pg. 301 – 306 • Obj: Learn how to write and graph an equation of a direct variation. • Standards: A.CED.2 and N.Q.2

  6. 5.2 Direct Variation • Direct variation – a relationship that can be represented by the function y=kx • Constant of Variation for a direct variation – k • Graphs of Direct Variation • The line passes through (0,0) • The slope of the line is k

  7. 5.3 Slope-Intercept Form • Pg. 308 – 314 • Obj: Learn how to write and graph linear equations using slope-intercept form. • Content Standards: F.IF.7.a, A.SSE.1.a, A.SSE.2, A.CED.2, F.IF.4, F.BF.1.a, F.BF.3, F.LE.2, F.LE.5

  8. 5.3 Slope-Intercept Form • Parent Function – the simplest function of a group of functions with common characteristics • Linear Parent Function – y = x or f(x) = x • Linear Equation – an equation that models a linear function • Y-intercept – the y-coordinate of a point where the graph crosses the y-axis • Slope-Intercept Form – y=mx + b • m – slope • b – y-intercept

  9. 5.3 Slope-Intercept Form • Method for graphing • Identify the slope and y-intercept • Graph the y-intercept • Use the slope to find one more point • Connect the points with a straight edge • Method for writing an equation • Identify the slope and y-intercept • Substitute into the slope-intercept form

  10. 5.4 Point-Slope Form • Pg. 315 – 320 • Obj: Learn how to write and graph linear equations using point-slope form. • Standards: F.LE.2, A.SSE.1.a, A.SSE.2, A.CED.2, F.IF.4, F.IF.7.a, F.BF.1.a, F.BF.3, F.LE.5

  11. 5.4 Point-Slope Form • Point-Slope Form of a Linear Equation • m – slope • (x1, y1) – point on the line

  12. 5.5 Standard Form • Pg. 322- 328 • Obj: Learn how to graph linear equations using intercepts and how to write linear equations in standard form. • Standards: A.CED.2, N.Q.2, A.SSE.2, F.IF.4, F.IF.7.a, F.IF.9, F.BF.1.a, F.LE.2, F.LE.5

  13. 5.5 Standard Form • X-intercept – the x-coordinate of a point where a graph crosses the x-axis • Standard Form of a Linear Equation • Ax +By = C • A, B, and C are real numbers • A and B are not both zero • Graphing using the intercepts • x-intercept – let y=0 and solve for x • y-intercept – let x=0 and solve for y

  14. 5.5 Standard Form • Linear Equations • Slope-intercept – y=mx+b • Point-slope – y – y1=m(x-x1) • Standard – Ax + By = C

  15. 5.5 Concept Byte • Pg. 329 • Inverse of a Linear Function • Standard: F.BF.4.a

  16. 5.5 Concept Byte • Inverse Function – A function that pairs b with a whenever f pairs a with b • Method for the Inverse Function • Replace f(x) with y • Switch x for y and y for x • Solve for y • Write in function notation, using f^-1 to represent the inverse of the function f

  17. 5.6 Parallel and Perpendicular Lines • Pg. 330 – 335 • Obj: Learn how to determine whether lines are parallel, perpendicular, or neither, and how to write equations of parallel and perpendicular lines. • Standard: G.GPE.5

  18. 5.6 Parallel and Perpendicular Lines • Parallel lines – lines in the same plane that never intersect – have the same slope • Perpendicular lines – lines that intersect to form right angles – have opposite reciprocal slopes • Opposite reciprocals – two numbers whose product is -1

  19. 5.7 Scatter Plots and Trend Lines • Pg. 336 – 343 • Obj: Learn how to write an equation of a trend line and a line of best fit and how to use a trend line and a line of best fit to make predictions. • Standards: S.ID.6.c, N.Q.1, F.LE.5, S.ID.6.a, S.ID.7, S.ID.8, S.ID.9

  20. 5.7 Scatter Plots and Trend Lines • Scatter Plot – a graph that relates two different set of data by displaying them as ordered pairs • Positive Correlation – y increases as x increases • Negative Correlation – y decreases as x increases • No Correlation – when x and y are not related • Trend Line – a line on a scatter plot, drawn near the points, that shows a correlation • Interpolation – estimating a value between two known values

  21. 5.7 Scatter Plots and Trend Lines • Extrapolation – predicting a value outside the range of known values • Line of Best Fit – a trend line that shows the relationship between two sets of data most accurately • Correlation Coefficient – a number from -1 to 1, that tells you how closely the equation models the data • Causation – when a change in one quantity causes a change in a second quantity

  22. 5.7 Concept Byte • Pg. 344 – 345 • Using Residuals • Content Standard: S.ID.6.b

  23. 5.7 Concept Byte • Residual – the difference between the y-value of a data point and the corresponding y-value of a model for the data set

  24. 5.8 Graphing Absolute Value Functions • Pg. 346 – 350 • Obj: Learn how to graph an absolute value function and to translate the graph of an absolute value function. • Content Standards: F.BF.3, and F.IF.7.b

  25. 5.8 Graphing Absolute Value Functions • Absolute Value Function – has a V shaped graph that opens up or down • Translation – a shift of a graph horizontally, vertically, or both • Piecewise Function – a function that has different rules for different parts of a domain • Step Function – a function that pairs every number in an interval with a single value

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