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Chapter 1: Linear Functions V. J. Motto M110 Modeling with Elementary Functions 1.1 Review of Linear Functions 1.2 Introduction to TI-83+ 5/24/2017 V. J. Motto 1 Housekeeping Essay Assignment Getting Help Come visit me! Mathematics Laboratory Dana 208 Office Hours MWF 1000 – 1100 Room Dana 220/208 MWF 1330 – 1400 Room UT 306, Dana 220 or Dana 208 By Appointment 5/24/2017 V. J. Motto 2 Rectangular Coordinate System Note the x-axis and y-axis. The cross at the point (0, 0) or the Origin. There are 4 quadrants numbered counter clockwise with Roman Numerals. 5/24/2017 V. J. Motto 3 Coordinates (x, y) To plot or graph the point that corresponding to the ordered pair (a, b) we start at the origin and move a units left or right. Then we move b units up or down. 5/24/2017 V. J. Motto 4 Graphing y = - 300x + 2000 Value (dollars) Computer Value 2500 2000 1500 1000 500 0 Series1 0 2 4 6 Time (years) 5/24/2017 V. J. Motto 5 Example: Graphing y = 3x - 5 Lets use our TI-83+ to sketch the graph 5/24/2017 y = button Graph button 2nd Graph Table V. J. Motto 6 Linear Equations A linear equation in two variables is an equation that can be written in the form Ax + By = C Where A, B, and C are real numbers and A and B are not both 0. The graph of a linear equation in two variable is a straight line. 5/24/2017 V. J. Motto 7 Comment Often, it is more convenient to solve the equation for y. Thus, the linear equation 3x + y = 4 would be manipulate to become y = - 3x + 4 which is easier to use when creating tables. You choose different x values and calculate the corresponding y values. 5/24/2017 V. J. Motto 8 Example: Graphing – 5x + 3y = 15 5 x 3 y 15 3 y 5 x 15 5 y x 5 3 5/24/2017 V. J. Motto 9 Forms of Linear Equations Form Ax + By = C y = mx + b y – y1 = m(x - x1) 5/24/2017 Description Standard Form. A and B are not both 0 Slope-intercept Form. Slope is m; y-intercept is (0, b) Point-slope Form Slope is m; (x1, y1) is a point of the line y=c Horizontal Line Slope is 0; y-intercept is (0, c) x=c Vertical Line Slope is undefined; x-intercepet is (c, 0) V. J. Motto 10