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

5.1 Rate of Change and Slope Types of Slope ▫Positive ▫Negative ▫Zero ▫Undefined

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

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

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

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

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

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

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

5.5 Standard Form Pg 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

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

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

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

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

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

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

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

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

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

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

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

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

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