Converting Linear Equations into Different Forms SlopeIntercept Form

Converting Linear Equations into Different Forms: Slope-Intercept Form and Standard Form

Slope intercept form is: y = mx + b • m is slope • b is y-intercept • x is input • y is output

Standard form is: Ax + By = C • • A, B and C will be numbers x and y are the variables A, B and C must be integers A (the leading coefficient) must be positive ie. 7 x – 6 y = 12 Not -3 x + 9 y = 4 Not 15 x + 4. 5 y = -3 why not? Fix it:

Convert Into Slope-Intercept Form (divide both sides by 2 to get y alone) 2 (now simplify all fractions) 1

Convert From Standard Form Into Slope-Intercept Form 21 x – 7 y =14 -7 y = -21 x + 14 (subtract 21 x from both sides) (now divide both sides by -7) (simplify all fractions) y = 3 x – 2

Convert From Standard Form Into Slope-Intercept Form 4 x+3 y=24 -4 x 3 y=-4 x+24 3 3 3

Convert From Slope-Intercept Form Into Standard Form y = -1/3 x + 7 + 1/ 3 x + 1 / 3 x 1/ 3 3 x +y=7 3 3 x + 3 y = 21 (put in Ax + By = C) (add 1/3 x to both sides) Standard form must have a positive leading coefficient (A) and A, B, and C must be integers, so clear out the fractions by multiplying every term by 3

Convert From Slope-Intercept Form Into Standard Form y = 2. 5 x + 1 -2. 5 x + y = 1 -2 -2 -2 5 x - 2 y = -2 (subtract 2. 5 x from both sides) Standard form must have a positive leading coefficient (A) and A, B, and C must be integers, so clear out the negative decimal by multiplying every term by -2

Convert to Slope-Intercept Form: 5 y = 15 + 10 x (divide both sides by 5 to get y alone) 5 y = 15 + 10 x (now simplify all fractions) (write in y=mx+b order) y = 2 x + 3

Convert Into Slope-Intercept Form 2 y + 26 = -6 x (subtract both sides by 26) (now divide both sides by 2 2 y = -6 x - 26 (simplify all fractions) y = -3 x - 13

Convert Into Slope-Intercept Form 2 x = 5 y - 10 • 2 x = 5 y-10 -5 y • 2 x – 5 y = -10 -2 x • -5 y = -2 x – 10 -5 -5 -5 • y = 2/ 5 x + 2