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# Module 4

### Variation and Problem Solving

What way does x and y go on a graph? | x is horizontal and y is vertical |

which of these points are x and y? (-2,1) | x=-2; y=1 (x,y) |

how to find coordinates for: f(x)=2x | pick a number for x and plug into the formula to find y. if x=1, then y=2 [f(1)=2(1)] [(1,2)] if x=0, then y=0 [f(0)=2(0)] [(0,0)] |

what is the function notation equation | y=mx+b |

what is line function notation | f(x)=mx+b |

what are the parts of y=mx+b | m= slope b= y intercept |

how to place "slope 2; y intercept (0,1)" into line function notation equation | f(x)=mx+b place in 2 for m and 1 for b f(x)=2x+1 |

point-slope equation | y-y1 = m(x-x1) |

how to find equation of a line when slope 3; through (3,1) | plug into point slope equation y-1=3(x-3) y-1=3x-9 y=3x-8 |

how to find slope | y2-y1 m= ------------ x2-x1 |

how to write the equation of a line without slope (-4,-3) (-8,-2) | find slope (-2)-(-3) m= ------------ m=1/-4 (-8)-(-4) y-(-3)=-1/4(x-(-4)) y+3=-1/4x-1 y= -1/4x-4 |

when two nonvertical lines are parallel... | if they have the same slope and different y intercept |

how to find the equation of a line that goes through (1,1) and is parallel to y=5x+3 | we know that m=5, since they are parallel. use point slope equation y-1=5(x-1) y-1=5x-5 y=5x-4 |

to find the slope of a new line that is perpendicular... | take the negative reciprocal of slope (m) |

how to write the equation of the line (-10,8) that is perpendicular to 2y=x-6 | divide 2y=x-6 by 2 y=1/2x-3 take the negative reciprocal of slope m=-2 put into point slope equation y-8= -2(x+10) y-8= -2x-20 y= -2-12x |

what is standard form | x+y= # |

write into equation and put into standard form slope 6; (-6,9) | y-9=6(x+6) y=6x+45 6x-y=-45 |