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Download 3.5: The Point-Slope Form of a Linear Equation
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Transcript
Intermediate Algebra Finding Equations of Lines Name _____________________________ Finding equations from graphs: steps: 1. Find the y-intercept. (0, b) 2. Find the slope. m Ex 1: Slope: down 1, right 1 m = -1 y-int: (0, 5), so b=5 Therefore, rise run y x 5 f ( x) x 5 3. Plug into slope-intercept formula y mx b . Ex 2: Slope: up 1, right 2 m=½ y-int: (0, 2), so b=2 Therefore, 1 x2 2 1 f ( x) x 2 2 y 4. Put into function notation by replacing y with f(x). f ( x) mx b You try: Find the equations of each line. y y y y (0,6) (0, 3) (-3,0) (10,0) x (-7,0) _________________ x x x (0,-4) _________________ Finding Equations given a point and a slope: steps: 1. Plug the point ( x1 , y1 ) and the slope, m, that was given into the point-slope formula y y1 m( x x1 ) . 2. Solve for y to get into slope intercept form: y mx b . 3. Put into function notation by replacing y with f(x). f ( x) mx b _________________ __________________ Ex: Write an equation for a line with slope, 1 m , and goes through the point (8, -2). 2 You try: Find the equation of each line. 3 , 5 2. Write an equation for the line with slope, 3 m , and goes through the point (-8, 0). 4 3. Write an equation for the line with slope, m 0 , and goes through the point (5, -4). 4. Write an equation for the line with slope, m undefined , and goes through the point (2, 7). 1. Write an equation for the line with slope, m and it goes through the point (-10, -2). Finding Equations given 2 points: steps: y y1 1. Calculate the slope. m 2 x2 x1 2. Use the slope, m, and choose either point to plug into the point-slope formula y y1 m( x x1 ) . 3. Solve for y to get into slope intercept form: y mx b . 4. Put into function notation by replacing y with f(x). f ( x) mx b Ex: Write an equation for a line that goes through the points (4, -3) and (-6, 2). You Try: Find the equation of each line. 1. Write an equation for the line that goes through the points (6, -2) and (-3, 4). 2. Write an equation for the line that goes through the points (-7, -3) and (-6, -4). 3. Write an equation for the line that goes through the points (-3, -2) and (-3, 4). 4. Write an equation for the line that goes through the points (6, 4) and (-3, 4). Finding Equations that Parallel or Perpendicular to Other Equations: steps: Ex: Write an equation for the line that goes 1. Put the equation given in slope intercept form through the point (-6, 4) and perpendicular to to determine the slope, m. the graph of 2 x 3 y 9 . 2. Use the slope, m, to find the parallel or perpendicular slope For parallel lines: -use the same slope, m For perpendicular lines: -use the negative reciprocal of m 3. Plug the point ( x1 , y1 ) and the parallel or perpendicular slope, m, that was found in step#2 into the point-slope formula y y1 m( x x1 ) . 4. Solve for y to get into slope intercept form: y mx b . 5. Put into function notation by replacing y with f(x). f ( x) mx b You Try: Find the equation of each line. 1. Write an equation for the line that goes through the point (6, -1) and parallel to the graph of 2 x 3 y 12 . 3. Write an equation for the line that goes through the point (-4, 5) and perpendicular to the graph of 3 y 15 . 5. Write an equation for the line that goes through the point (2, 3) and parallel to the line that goes through the points (2, 8) and (4, 0). 2. Write an equation for the line that goes through the point (-2, 2) and perpendicular to the graph of 4x 2 y 6 . 4. Write an equation for the line that goes through the point (3, -7) and parallel to the graph of x 2 . 6. Write an equation for the line that goes through the point (6, 9) and perpendicular to the line that goes through the points (0, -2) and (-5, 8).