Lesson: Finding Equations

Sometimes you will need to write the equation Sometimes you will need to write the equation given information about the graph. Sometimes you will need to write the equation To do this you have to use this equation: given information about the graph. Sometimes you will need to write the equation To do this you have to use this equation: given information about the graph. y - y _{1} = m(x - x_{1})Sometimes you will need to write the equation To do this you have to use this equation: which is the point-slope form given information about the graph. y - y _{1} = m(x - x_{1})Point-slope Form y - y _{1} = m(x - x_{1})? y - y _{1} = m(x - x_{1})Point-slope Form ? To use the point slope form you need three values y - y _{1} = m(x - x_{1})To use the point slope form you need three values An x _{1}y - y _{1} = m(x - x_{1})To use the point slope form you need three values An x _{1}y - y _{1} = m(x - x_{1})To use the point slope form you need three values An x _{1}An y _{1}y - y _{1} = m(x - x_{1})To use the point slope form you need three values An x _{1}An y _{1}y - y _{1} = m(x - x_{1})To use the point slope form you need three values An x _{1}and an m An y _{1}y - y _{1} = m(x - x_{1})To use the point slope form you need three values An x _{1}and an m An y _{1}y - y _{1} = m(x - x_{1})You will never ever EVER put numbers in for the x and y y - y _{1} = m(x - x_{1})You will never ever EVER put numbers in for the x and y y - y _{1} = m(x - x_{1})You will never ever EVER put numbers in for the x and y y - y _{1} = m(x - x_{1})never You will never ever EVER put numbers in for the x and y y - y _{1} = m(x - x_{1})never You will never ever EVER put numbers in for the x and y ever y - y _{1} = m(x - x_{1})never Mark all variables that will be replaced with numbers y - y _{1} = m(x - x_{1})y y _{1}m x x _{1}Mark all variables that never EVER be replaced with y - y _{1} = m(x - x_{1})y y _{1}m x x _{1}numbers So if they give you a point So if they give you a point (2,3) So if they give you a point and a slope (2,3) So if they give you a point and a slope (2,3) 4 You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope (2,3) 4 You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope x _{1}(2,3) 4 You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope x _{1}(2,3) 4 y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope x _{1}(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y - y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y - 3 y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y - 3 = y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y - 3 = 4 y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y - 3 = 4( y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y - 3 = 4(x y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y - 3 = 4(x - y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y - 3 = 4(x - 2 y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}You will use that to find x _{1}, y_{1}, and m.So if they give you a point and a slope and then plug in those values in x _{1}y - 3 = 4(x - 2) y - y _{1} = m(x - x_{1})(2,3) 4 m y _{1}y - y _{1} = m(x - x_{1})x _{1} = 1y _{1} = 4m = 5 y - 4 ? = 5 ? ( x - 1 ? ) Slope: Point: ( 5 1 , 4 ) y - y _{1} = m(x - x_{1})x _{1} = 3y _{1} = 8m = 2 y - 8 ? = 2 ? ( x - 3 ? ) Slope: Point: ( 2 3 , 8 ) y - y _{1} = m(x - x_{1})x _{1} =y _{1} =m = y 1 ? 9 ? 5 ? - 9 = 5 ( x - 1 ) Slope: Point: ( 5 1 , 9 ) y - y _{1} = m(x - x_{1})x _{1} =y _{1} =m = y -2 ? -3 ? -6 ? + 3 = -6 ( x + 2 ) Slope: Point: ( -6 -2 , -3 ) y - y _{1} = m(x - x_{1})x _{1} = 6y _{1} = 1m = 4 y - 1 = 4 ( x - 6 ) Slope: Point: ( 4 ? 6 ? , 1 ? ) Sometimes they will give you 2 points Sometimes they will give you 2 points and ask you to find the equation Sometimes they will give you 2 points and ask you to find the equation ( 7 , 3 ) Sometimes they will give you 2 points and ask you to find the equation ( 7 , 3 ) ( 6 , 2 ) You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points and ask you to find the equation ( 7 , 3 ) ( 6 , 2 ) You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points and ask you to find the equation x _{1}( 7 , 3 ) ( 6 , 2 ) You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points and ask you to find the equation x _{1}( 7 , 3 ) ( 6 , 2 ) y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points and ask you to find the equation x _{1}( 7 , 3 ) ( 6 , 2 ) y _{1}no m? You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula and ask you to find the equation x _{1}( 7 , 3 ) ( 6 , 2 ) y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) y _{2}y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = y _{2}y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = y _{2}y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 y _{2}y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - y _{2}y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 y _{2}y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 y _{2}y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - y _{2}y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 y _{2}y _{1}You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 y _{2}y _{1}= You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 y _{2}y _{1}= -1 -1 You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 y _{2}y _{1}= -1 -1 = You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation x _{1}x _{2}y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 y _{2}y _{1}= -1 -1 = 1 You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = -1 -1 = 1 x _{1} = 7You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = -1 -1 = 1 x _{1} = 7y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y - -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y - 3 -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y - 3 = -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y - 3 = 1 -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y - 3 = 1( -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y - 3 = 1(x -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y - 3 = 1(x - -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y - 3 = 1(x - 7 -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y - 3 = 1(x - 7) -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3You need an x _{1}, y_{1}, and an mSometimes they will give you 2 points To find the m you must use the slope formula m = and ask you to find the equation y _{2} - y_{1}x _{2} - x_{1}( 7 , 3 ) ( 6 , 2 ) = 2 - 3 6 - 7 = y - 3 = 1(x - 7) -1 -1 = 1 x _{1} = 7m = 1 y _{1} = 3y _{2} =x _{1} =y _{1} =x _{2} =m = m = 7 ? y _{2} - y_{1}x _{2} - x_{1}8 ? 4 ? 3 ? 7 4 - - 8 3 = -1 ? 1 ? Point 1: Point 2: ( ( 3 4 , , 8 7 ) ) y _{2} =x _{1} =y _{1} =x _{2} =m = m = 4 ? y _{2} - y_{1}x _{2} - x_{1}1 ? 7 ? 2 ? 4 7 - - 1 2 = 3 ? 5 ? Point 1: Point 2: ( ( 2 7 , , 1 4 ) ) y _{2} =x _{1} =y _{1} =x _{2} =m = m = 8 ? y _{2} - y_{1}x _{2} - x_{1}9 ? 7 ? 6 ? 8 7 - - 9 6 = -1 ? 1 ? Point 1: Point 2: ( ( 6 7 , , 9 8 ) ) They may ask you for the equation of a line They may ask you for the equation of a line parallel to a given line They may ask you for the equation of a line parallel to a given line y = 3x +2 given line They may ask you for the equation of a line parallel to a given line y = 3x +2 through a given point They may ask you for the equation of a line parallel to a given line y = 3x +2 through a given point (1,4) given point They may ask you for the equation of a line parallel to a given line y = 3x +2 through a given point x _{1}(1,4) y _{1}They may ask you for the equation of a line parallel to a given line y = 3x +2 through a given point m x _{1}(1,4) y _{1}They may ask you for the equation of a line parallel to a given line y = 3x +2 through a given point m x _{1}(1,4) y _{1}y - y _{1} = m(x - x_{1})They may ask you for the equation of a line parallel to a given line y = 3x +2 through a given point m x _{1}(1,4) y _{1}y - y _{1} = m(x - x_{1})y - 4 = 3(x - 1) |

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