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Chapter 6 Coordinate Geometry. 6.5. Linear Equations: Point-Slope Form. 6.5. 1. MATHPOWER TM 10, WESTERN EDITION. Writing Equations in Standard Form. When the equation of a line is written in the form Ax + By + C = 0 , the equation is in Standard Form.
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Chapter 6 Coordinate Geometry 6.5 Linear Equations: Point-Slope Form 6.5.1 MATHPOWERTM 10, WESTERN EDITION
Writing Equations in Standard Form When the equation of a line is written in the form Ax + By + C = 0, the equation is in Standard Form. For an equation to be in standard form: A, B and C are integers. A is a positive integer. A and B cannot both be zero. To write an equation of a line, you need: 1. the slope of the line 2. a point on the line 6.5.2
Writing the Equation of a Line Use the slope formula where: •(x, y) represents any point on the line, and •(x1, y1) refers to the given point. y - y1 = m(x - x1) The equation y - y1 = m(x - x1) is the point-slope form. 6.5.3
Writing an Equation Given a Point and a Slope Write an equation in standard form for the line through (6, -2) with slope of . (x1, y1) y - y1 = m(x - x1) (x - 6) y - (-2) = y - (-2) = 4[ ] 4[ ] (x - 6) 4(y + 2) = 3(x - 6) 4y + 8 = 3x - 18 0 = 3x - 4y - 26 3x - 4y - 26 = 0 Standard form of the equation Write an equation in standard form for the line through (-2, 7) with slope of . 2x + 3y - 17 = 0 6.5.4
Writing an Equation Given Two Points Find the equation, in standard form, of the line that passes through the points A(3, -4) and B (5, 6). Using the point B(3, -4): y - y1 = m(x - x1) y - (-4) = 5(x - 3) y + 4 = 5x - 15 0 = 5x - y - 19 5x - y - 19 = 0 Using the point B(5, 6): y - y1 = m(x - x1) m = 5 y - 6 = 5(x - 5) y - 6 = 5x - 25 0 = 5x - y - 19 5x - y - 19 = 0 6.5.5
Writing the Equation from the Graph (0, 5) (5, 0) m = -1 y - y1 = m(x - x1) y - 0 = -1(x - 5) y = -x + 5 x + y - 5 = 0 6.5.6
Assignment Suggested Questions: Pages 282 and 283 1 - 13 odd, 17, 21, 27, 29, 32 37 - 40, 46, 49, 50, 52, 53 6.5.7