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Algebra 1 Chapter 5 Standard form, point slope form, and slope intercept Perpendicular lines
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Standard Form Must write the equation in the form Ax+By=C Find 2 points on the line whose coordinates are both integers Use the values of the coordinates to fine the slope of the line using the formula m=y2-y1/x2-x1
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Standard Form Contâ€¦. Use values found for slope and a coordinates Then write it in point-slope form y-y1=m(x-x1) Solve for y
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Standard Form Contâ€¦. Example: M= 5, (6,3) Y-3=5(x-6) Write equation Y-3=5x-30 Distribute the 5 Y=5x-27 Add 3 to both sides
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Standard Form Contâ€¦. Then to make it into standard form we may need to add or subtract from either side Example: Y=5x-27 Add 27 to both sides Y+27=5x Subtract y from both sides 27=5x-y This is in Standard Form
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Recap Point-slope form y-y1=m(x-x1) Standard Form Ax+By=C Slope formula m=y2-y1/x2-x1
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Slope Intercept Form An equation of the line with slope m and y-intercept To find y-intercept, find where the point crosses the y-axis or where x=0 Itâ€™s the y-intercept of that point Ex: (0,5) so the intercept is 5
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Slope Intercept Form Contâ€¦. Then use slope formula m=y2-y1/x2-x1 Use the point that you found for the y-intercept Then find another point whose coordinates are integers
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Slope Intercept form Contâ€¦. Once you have found the y-intercept Also once found the slope Plug each one into the formula y=mx+b in the correct places
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Slope Intercept Form Contâ€¦. Example: Given points (0,6) (3,12) Find the slope and the y-intercept M=12-6/3-0=6/3=2 Plug into y=mx+b
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Slope Intercept Form Contâ€¦. Use the point that crosses the y-axis M=2, y-intercept=6 y=2x+6 Remark: positive slope rises left to right, negative slope falls left to right
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Perpendicular Lines To find a line perpendicular to another First we need to know the slope of the first line Perpendicular lines have the opposite reciprocal of the normal line
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Perpendicular Lines Contâ€¦ Once found the slope of the perpendicular line Use the point slope equation to find the equation of that line Then solve for y and put in slope intercept form
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Perpendicular Lines Contâ€¦. Example: Given two points (5,10) (8,16) Find the equation of the normal and perpendicular First: Find the slope of the normal line
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Perpendicular Lines Contâ€¦. M=16-10/8-5=6/3=2 Plug into point slope to find equation of the normal line, pick either point M=2 (5,10) y-10=2(x-5) y-10=2x-10 y=2x
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Example Contâ€¦. Now find the perpendicular line The slope is opposite and the reciprocal of the normal M=-1/2, then just pick a point again and plug it into point slope formula
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Example Contâ€¦. M=-1/2, (5,10) Y-10=-1/2(x-5) Y-10=-1/2x+5/2 Y=-1/2x+25/2 Now we have both equations
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