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Equations of Lines

Equations of Lines

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Equations of Lines

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  1. Equations of Lines Lesson 2.2

  2. Point Slope Form (x2, y2) • m • We seek the equation, given point and slope • Recall equation for calculating slope, given two points • Now multiply both sides by (x1 – x2) • Let any point (x,y) on the line be one of the points in the equation

  3. Point Slope Form • Alternative form • Try it out … • For a line through point (6, -2) and slope m = -3/4 determine the equation. • Show both forms (6, -2) •

  4. Slope Intercept Form • Recall that we have used y = m * x + b • The b is the y-intercept • Where on the y-axis, the line intersects • m is the slope • Given slope • Observe y-intercept

  5. Converting Between Forms • What does it take to convert from point slope formto slope-intercept form? • Multiply through the (x – x1) by m • Simplify the expression • Try it Note that this also determines the value for the y-intercept, b

  6. Two Point Form • Given (3, -4) and (-2, 12), determine the equation • Find slope • Use one of the points in the point-slope form

  7. Set the style of one of the equations to Thick Parallel Lines • Given the two equationsy = 2x – 5y = 2x + 7 • Graph both equations • How are they the same? • How are they different?

  8. Parallel Lines • Different: where they cross the y-axis • Same: The slope • Note: they are parallel Parallel lines have the same slope y=2x+7 y=2x-5 Lines with the same slope are parallel

  9. Perpendicular Lines • Now consider • Graph the lines • How are they different • How are they the same?

  10. Perpendicular Lines • Same: y-intercept is the same • Different: slope is different • Reset zoomfor square • Note lines areperpendicular

  11. Perpendicular Lines • Lines with slopes which are negative reciprocals are perpendicular • Perpendicular lines have slopes which are negative reciprocals

  12. Horizontal Lines • Try graphing y = 3 • What is the slope? • How is the line slanted? • Horizontal lines have slope of zero y = 0x + 3

  13. Vertical Lines • Have the form x = k • What happens when we try to graph such a line on the calculator? • Think about • We say “no slope” or “undefined slope” • k

  14. Assignment • Lesson 2.2A • Page 88 • Exercises 1 – 73 EOO

  15. Direct Variation • The variable y is directly proportional to x when:y = k * x • (k is some constant value) • Alternatively • As x gets larger, y must also get larger • keeps the resulting k the same

  16. Direct Variation • Example: • The harder you hit the baseball • The farther it travels • Distance hit is directlyproportional to theforce of the hit

  17. Direct Variation • Suppose the constant of proportionality is 4 • Then y = 4 * x • What does the graph of this function look like? • Note: • This is a linear function • The constant of proportionality is the slope • The y-intercept is zero

  18. Applications • Math whiz Horatio Al-Jebra rides a bicycle on a straight road away from town. • The graph shows his distance y in miles from town after x hours • How fast is he riding? • Find • How far from towninitially • How far from townafter 3 hours and 15 min. Distance (miles)

  19. Assignment • Lesson 2.2B • Page 109 • Exercises 75 – 109 EOO