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Point Slope Equation of a Line

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Any time you are given the slope of a line (m) and a point on the line ( x 1, y 1 ) Use the point-slope equation of a line to solve. y – y 1 = m ( x – x 1 )

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Point Slope Equation of a Line m = 5; ( 2, 3 ) Use the point-slope equation of a line to solve. y – y 1 = m ( x – x 1 ) y – 3 = 5 ( x – 2 )

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Slope-intercept Equation of a Line y – 3 = 5 ( x – 2 ) y – 3 = 5x – 10 y = 5x – 7 This is the slope-intercept equation of the line with a slope of 5 passing through the point ( 2, 3 )

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Standard Equation of a Line y = 5x – 7 This is the slope-intercept equation of the line with a slope of 5 passing through the point ( 2, 3 ) If they want the answer in standard form Ax + By = C just rearrange the furniture! - 5x + y = -7

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A matter of style - 5x + y = -7 Some textbook authors dislike starting with a negative. Although this is a correct answer, if it is not included in the multiple choice answers, clean it up by multiplying everything by -1. 5x – y = 7

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Oh no! A Fraction! What if the slope is a fraction? M = 2 / 3 ; ( - 7, - 5 ) We still use y – y 1 = m ( x – x 1 )

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Oh no! A Fraction! y – y 1 = m ( x – x 1 ) Notice how I use parentheses to keep my signs straight!

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Clean up the double signs

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Fractions and Equal Signs Whenever you have a fraction and an equal sign, multiply both sides of the equation by the LCD.

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Fractions and Equal Signs

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Finish Up! Answer in slope-intercept form

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Finish Up! Answer in standard form with no leading negative.

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Point- slope equation of a line 1.If you know a point ( x 1, y 1 ) and the slope m. 2.Use y – y 1 = m ( x – x 1 ) 3.Distribute the m 4.Move the y 1 5.This gives the slope-intercept equation of the line. 6.If they want it in standard form, rearrange the furniture ( and you may have to clear a leading negative).

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