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Mastering Linear Functions: A Comprehensive Guide

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Chapter 2 covers linear functions, including domain and range identification, standard form equations, slope determination, intercept finding, best fit line, parent function graphing, and inequality representation. Learn essential concepts for mathematical success!

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Mastering Linear Functions: A Comprehensive Guide

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  1. Chapter 2 Chapter 2 consists of linear functions. This chapter includes identifying the domain and range. This chapter also includes writing equations in standard form, finding the slope of a line, writing equations, finding the x and y-intercepts, finding the line of best fit, graphing a parent function, and writing and graphing inequalities. By: Brian G. Ernesto R. Alex R. Erick R.

  2. Vocabulary Linear Relation - A relation that can be graphed as a line. Non-Linear Relation - A relation that cannot be graphed as a line. Linear Equation – An equation that contains positive, negative, a variable, and a constant. Slope-Intercept Form – In the form of y=mx+b Standard Form – In the form of ax+by=c Y-Intercept – Where the line intersects the Y-Axis. X-Intercept – Where the line intersects the X-Axis. Slope – A change in Y over a change in X. Domain – A set of the X-Coordinates. Range – A set of the Y-Coordinates. Discrete Relation – Graphed as a set of individual points. Continuous Relation – Graphed with a small curve. Independent Variable – The variable whose values make up the domain. Dependent Variable – The variable whose values make up the range. Transformation – Shift to the graph. Linear Function – A diagonal line. Constant – A vertical or horizontal line. Absolute Value Function – Graphed as a “V.” Quadratic Function - Parabola

  3. Note-Card Standard Form: ax + by = c Slope-Intercept Form: y = mx+ b

  4. Examples!!!!!! • 1.Identify a domain and range (using a graphing calc): y= x^2 -6x+ 4 • 2.Write an equation given two points: ( 4,6) and (2, 1) • 3.Write an equation given a slope and point: Slope: -1/3 through (-6,1) • 4.Find x – and y – intercepts: -6x+3y= 24

  5. More examples!! • 5.Find a slope given 2 points: (3,-5) and (-1,7) • 6. Write an equation in standard form: y=2/3x-8

  6. Solutions • 1. • 2. (1-4)/ (2-6)= -3/-4= ¾, (y-6)=3/4(x-4), y-6=3/4x-3, y=3/4x+3 • 3. y-1= = -1/3(x- -6), y-1=-1/3x+2, y=-1/3x+3 • 4. -6x+0=24, x= -4, 0x+3y=24, y=8 • 5.(7+5)/(-1-3), 12/-4, -3 • 6. (3)y= 2/3x-8(3), 3y=2x-24, -2x+3y=-24

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