Three forms for describing linear functions using equations.

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Presentation transcript:

Three forms for describing linear functions using equations.

y = mx + b (y –y 1 ) = m(x – x 1 ) General form Ax + By + C = 0 A, B and C are real numbers. A and B cannot be zero. A must be a whole number. Slope y intercept form. Slope point form

Slope and one pointSlope y interceptGeneral form m = -3, ( -2, 5) (y -5) = -3( x – (-2)) (y -5) = -3 (x + 2) y = mx + b (y –y 1 ) = m(x – x 1 ) Ax + By + C = 0 (y -5) = -3 (x + 2) y – 5 = -3x – 6 y = -3x – y = -3x - 1 (y -5) = -3 (x + 2) y – 5 = -3x – 6 y – 5 +6 = -3x y + 1 = -3x 3x + y + 1 = 0 y = -3x - 1 3x + y = -1 3x + y + 1 = 0 Same Given:

Math trick #1 Get rid of fractions by multiplying by the LCM. (y – (-4)) = -3/2 (x – 5) LCM = 2, multiply all terms by 2. 2(y – (-4)) = 2[-3/2 (x – 5) ] 2y + 8 = -3(x – 5) 2y + 8 = -3x x + 2y – 7 = 0

Math trick #2 Change negative sign in A to positive by multiplying by (-1) to all terms. -3x + 4y – 6 = 0 (-1) (-3x + 4y – 6 = 0) 3x – 4y + 6 = 0 Watch the sign changes! Integer rules apply.