By Berchie Holliday
Publication by means of Holliday, Berchie, Cuevas, Gilbert J., McClure, Melissa S.
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Extra resources for Advanced Mathematical Concepts: Precalculus with Applications
20 Chapter 1 Linear Relations and Functions y O ( 23, 0) (0, Ϫ2) 3x Ϫ y Ϫ 2 ϭ 0 x The slope of a nonvertical line is the ratio of the change in the ordinates of the points to the corresponding change in the abscissas. The slope of a line is a constant. y Slope The slope, m, of the line through (x1, y1) and (x2, y2) is given by the following equation, if x1 x2. mϭ (x1, y1) y2 Ϫ y1 m ϭ ᎏᎏ x2 Ϫ x1 y2 Ϫ y1 x2 Ϫ x1 (x2, y2) O x The slope of a line can be interpreted as the rate of change in the y-coordinates for each 1-unit increase in the x-coordinates.
When x ϭ 0, f(x) ϭ 5(0) ϩ 4, or 4. Thus, the coordinates of a second point are (0, 4). Chapter 1 Linear Relations and Functions f (x) ϭ 5x ϩ 4 O x b. f(x) ϭ Ϫ2 f (x) Since m ϭ 0 and b ϭ Ϫ2, this function has no x-intercept, and therefore no zeros. The graph of the function is a horizontal line 2 units below the x-axis. C HECK Communicating Mathematics FOR O x f (x) ϭ Ϫ2 U N D E R S TA N D I N G Read and study the lesson to answer each question. 1. Explain the significance of m and b in y ϭ mx ϩ b.
Write each equation in slope-intercept form. 03 53,473 1336 945 1336 y ϭ ᎏᎏx ϩ ᎏᎏ 53,473 1336 y ϭ Ϫᎏᎏx ϩ ᎏᎏ Since these equations are the same, their graphs coincide. As a result, any ordered pair that is a solution for the equation for the opening value is also a solution for the equation for the closing value. 03 at closing. In Lesson 1-3, you learned that any linear equation can be written in standard form. The slope of a line can be obtained directly from the standard form of the equation if B is not 0.
Advanced Mathematical Concepts: Precalculus with Applications by Berchie Holliday