Linear FunctionsChapter 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

12

12

change horizontal

change vertical

xx

yy

run

rise

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

)( 11 xxmyy

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

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