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# Algebra 1 Lesson Plan

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### Algebra 1 Lesson Plan

1. 1.  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
2. 2.  Use values found for slope and a coordinates  Then write it in point-slope form y- y1=m(x-x1)  Solve for y
3. 3.  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
4. 4.  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
5. 5.  Point-slopeform y-y1=m(x-x1)  Standard Form Ax+By=C  Slope formula m=y2-y1/x2-x1
6. 6.  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  It’s the y-intercept of that point Ex: (0,5) so the intercept is 5
7. 7.  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
8. 8.  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
9. 9.  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
10. 10.  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
11. 11.  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
12. 12.  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
13. 13.  Example: Given two points (5,10) (8,16)  Find the equation of the normal and perpendicular  First: Find the slope of the normal line
14. 14.  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
15. 15.  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
16. 16.  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