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Transcript
2.2 Equations of Lines 1 0011 0010 1010 1101 0001 0100 1011 2 45 Point-Slope Form of a Line 0011 0010 1010 1101 0001 0100 1011 The line with slope m passing through the point (x1, y1) has equation y y1 m( x x1 ) 1 2 45 Examples: a. Find an equation of the line with slope 1.7, passing through (-8, 10). b. Find an equation of the line passing through (-1, 2) and (-2, -3). Slope-Intercept Form of a Line 0011 0010 1010 1101 0001 0100 1011 The line with slope m and y-intercept b is given by y=mx+b 1 2 45 Example: Find the equation of a line with x-intercept -6 and y-intercept -8. 1 Finding x and yintercepts 0011 0010 1010 1101 0001 0100 1011 • To find the x-intercept, let y = 0 and solve for x. • To find the y-intercept, let x = 0 and solve for y. 1 2 45 Example: Find the x- and y-intercepts of 5x + 2y = -20. Sketch the graph. Horizontal & Vertical Lines 0011 0010 1010 1101 0001 0100 1011 • • • • The equation of a horizontal line is y = c. Horizontal lines have zero slope. The equation of a vertical line is x = c. Vertical lines have undefined slope. 1 2 45 • Example: Find an equation of the vertical line passing through (1.95, 10.7) Parallel and Perpendicular Lines 0011 0010 1010 1101 0001 0100 1011 • Parallel lines have the same slope. • Perpendicular lines have slopes which are negative reciprocals (unless one line is vertical) 1 2 45 From Precalculus with Modeling and Visualization 3rd ed. by Rockswold, 2006, p.93 2 Examples 0011 0010 1010 1101 0001 0100 1011 • Find an equation of the line parallel to the line y = – 4x – 12, passing through (2, -5). • Find an equation of the line perpendicular to x = 15, passing through (1.6, -9.5). • Find an equation of the line passing through (2, 8) and perpendicular to the line passing through (-3, -5) and (-4, 0). 1 2 45 3