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Unit 3 Part 2 Writing Equations Ax + By = C (standard form) y = mx + b (slope – intercept form)

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y = mx + b is a form of an equation What is the equation of a line that has a slope of ½ and a y-intercept of -3 ? y = mx + b y = ½ x – 3 Don’t forget the ‘x’

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Try these on your own. What is the equation of a line that has a slope of 2 and a y-intercept of -1 ? y = 2x – 1 What is the equation of a line that has a slope of ¾ and a y-intercept of 2 ? y = ¾ x + 2

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y = mx + b Write the equation of the line whose slope is 2 and contains the point ( 1, 5). 1 st substitute into the equation. y = mx + b 5 = (2)(1) + b 5 = 2 + b -2 -2 3 = b and ‘m’ = 2 y = 2x + 3

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y = mx + b Write the equation of the line whose slope is 3 and contains the point ( 2, 8). 1 st substitute into the equation. y = mx + b 8 = (3)(2) + b 8 = 6 + b -6 -6 2 = b and ‘m’ = 3 y = 3x + 2

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y = mx + b Write the equation of the line whose slope is -2 and contains the point ( 4, -9). 1 st substitute into the equation. y = mx + b -9 = (-2)(4) + b -9 = -8 + b +8 +8 -1 = b and ‘m’ = -2 y = -2x – 1

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y = mx + b Write the equation of the line whose slope is ½ and contains the point ( - 4, -3). 1 st substitute into the equation. y = mx + b -3 = ( ½ )(- 4) + b -3 = -2 + b +2 +2 -1 = b and ‘m’ = ½ y = ½ x – 1

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Write the equation of the line that contains these two points. ( 1, 3) ( 2, 6) 1 st Calculate the slope Now substitute y = mx + b 3 = 3(1) + b 3 = 3 + b -3 -3 0 = b y = 3x + 0 y = 3x 3 – 6 -3 1 – 2 -1 m = = = + 3

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Write the equation of the line that contains these two points. ( 3, 4) ( 5, 10) 1 st Calculate the slope Now substitute y = mx + b 4 = 3(3) + b 4 = 9 + b -9 -9 -5 = b y = 3x – 5 4 – 10 -6 3 – 5 -2 m = = = + 3

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Write the equation of the line that contains these two points. ( 4, -2) ( -8, 7) 1 st Calculate the slope Now substitute y = mx + b -2 = - ¾ (4) + b -2 = -3 + b +3 +3 +1 = b y = - ¾ x + 1 -2 – 7 -9 4 – (-8) 12 m = = = - 3 4

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Write the equation of the line that contains these two points. ( -6, -3) ( 0,-5) 1 st Calculate the slope Now substitute y = mx + b -3 = - ⅓ (-6) + b -3 = 2 + b -2 -2 -5 = b y = - ⅓ x – 5 -3 –(-5) 2 -6 – 0 -6 m = = = - 1 3

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Write the equation of the line that contains these two points. ( -2, -4) ( 2, -2) 1 st Calculate the slope Now substitute y = mx + b -4 = ½(-2) + b -4 = -1 + b +1 +1 -3 = b y = ½ x – 3 -4 – (-2) -2 -2 – 2 -4 m = = = + ½

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y – y = m ( x – x) Formula Write the equation of the line that has a slope of 2 and passes through the point ( -6, 4). 1 st substitute into the formula. y – y = m ( x – x) y – 4 = 2 ( x – (-6)) y – 4 = 2 ( x + 6 ) y – 4 = 2x + 12 + 4 + 4 y = 2x + 16 Can you do it ? Let’s see!

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y – y = m ( x – x) Formula Write the equation of the line that has a slope of -3 and passes through the point ( 1, -2). 1 st substitute into the formula. y – y = m ( x – x) y – (-2) = -3 ( x – 1) y + 2 = -3 ( x – 1 ) y + 2 = -3x +3 - 2 - 2 y = -3x + 1

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y – y = m ( x – x) Formula Write the equation of the line that has a slope of ½ and passes through the point ( 4, -3). 1 st substitute into the formula. y – y = m ( x – x) y – (-3) = ½ ( x – 4) y + 3 = ½ ( x – 4 ) y + 3 = ½x - 2 - 3 - 3 y = ½ x - 5

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y – y = m ( x – x) Formula Write the equation of the line that has a slope of -¾ and passes through the point ( 8, -1). 1 st substitute into the formula. y – y = m ( x – x) y – (-1) = -¾ ( x – 8) y + 1 = -¾ ( x – 8 ) y + 1 = -¾ x + 6 - 1 - 1 y = -¾ x + 5

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y – y = m ( x – x) Formula Write the equation of the line that has a slope of 3 and passes through the point ( -3, 2). 1 st substitute into the formula. y – y = m ( x – x) y – 2 = 3 ( x – (-3)) y – 2 = 3 ( x + 3 ) y – 2 = 3x + 9 + 2 + 2 y = 3x + 11

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