FINDING THE EQUATION OF A LINE

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Presentation transcript:

FINDING THE EQUATION OF A LINE KNOWN SITUATIONS: SLOPE & Y INTERCEPT SLOPE & 1 POINT TWO POINTS TRANSLATION

SLOPE & Y INTERCEPT HOW TO FIND EQUATION OF A LINE IF: You have SLOPE (a) and Y INTERCEPT (b) METHOD: SUBSTITUTE BOTH (a) and (b) in the equation. EXAMPLE: SLOPE is 2 3 and Y INTERCEPT is -1. y = 2 3 x - 1

SLOPE & 1 POINT HOW TO FIND EQUATION OF A LINE IF: You have SLOPE (a) and a POINT (x, y) METHOD: SUBSTITUTE for (a) and (x, y) in the equation. EXAMPLE: SLOPE is 2 and POINT is (3, 5) y = ax + b turns to 5 = 2(3) + b find for b 5 – 6 = b b = -1 therefore y = 2x – 1

TWO POINTS HOW TO FIND EQUATION OF A LINE IF: You have TWO POINTS (x1, y1) and (x2, y2) METHOD: PART A – FIND THE SLOPE PART B – SUBSTITUTE ONE OF THE POINTS + SLOPE (as in example 2) EXAMPLE: (1, 3) and (4, -6) a = y2 −y1 x2 −x1 = −6 −3 4 −1 = −9 3 = - 3

TWO POINTS SLOPE is – 3, then take one point (1, 3) or (4, -6) y = ax +b 3 = -3(1) + b then find for b 3 + 3 = b b = 6 therefore y = -3x + 6

TRANSLATION GENERAL STANDARD SLOPE Ax + By + C = 0 Ax + By = C y = Ax + B Any time you translate General form or Standard form to Slope form make sure you find for y (singular) Any time you translate General form to Standard form make sure you switch symbols for C as you send C to the other side of the = sign

TRANSLATION GENERAL FORM to SLOPE FORM 3x + 2y + 4 = 0 step 1 = isolate y 2y = -3x – 4 step 2 = find for y y = - 3 2 x – 2 SLOPE FORM TO GENERAL FORM y = - 3 2 x – 2 step 1= bring to one side 3 2 x +y + 2 = 0 step 2 = eliminate fractions 3x + 2y + 4 = 0

TRANSLATION STANDARD FORM to SLOPE FORM 2x + 3y = -2 step 1 = isolate y 3y = -2x – 2 step 2 = find for y y = - 2 3 x – 2 3 SLOPE FORM to STANDARD FORM y = - 2 3 x – 2 3 step 1 = bring x & y to 2 3 x + y = - 2 3 one side 2x + 3y = -2 step 2 = eliminate fraction