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

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