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## Equations of Lines

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**Equations of Lines**Lesson 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**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) •**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**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**Two Point Form**• Given (3, -4) and (-2, 12), determine the equation • Find slope • Use one of the points in the point-slope form**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?**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**Perpendicular Lines**• Now consider • Graph the lines • How are they different • How are they the same?**Perpendicular Lines**• Same: y-intercept is the same • Different: slope is different • Reset zoomfor square • Note lines areperpendicular**Perpendicular Lines**• Lines with slopes which are negative reciprocals are perpendicular • Perpendicular lines have slopes which are negative reciprocals**Horizontal Lines**• Try graphing y = 3 • What is the slope? • How is the line slanted? • Horizontal lines have slope of zero y = 0x + 3**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**Assignment**• Lesson 2.2A • Page 88 • Exercises 1 – 73 EOO**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**Direct Variation**• Example: • The harder you hit the baseball • The farther it travels • Distance hit is directlyproportional to theforce of the hit**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**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)**Assignment**• Lesson 2.2B • Page 109 • Exercises 75 – 109 EOO