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Various Forms of Lines

Various Forms of Lines. Slope Intercept Point Slope Form General Form/Standard Form. Slope Intercept Form. y = mx+b m is the slope b is the y intercept How do you find the x intercept? Set y=0 and solve for x. X and Y Intercept. y =.25x-3. Point Slope Form. (y-y 1 )=m(x-x 1 )

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Various Forms of Lines

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  1. Various Forms of Lines Slope Intercept Point Slope Form General Form/Standard Form

  2. Slope Intercept Form • y=mx+b • m is the slope • b is the y intercept • How do you find the x intercept? • Set y=0 and solve for x

  3. X and Y Intercept • y=.25x-3

  4. Point Slope Form • (y-y1)=m(x-x1) • To find x intercept, plug in zero for y • To find y intercept, plug in zero for x

  5. X Intercept • (y-2)=4(x+3)

  6. Y Intercept • (y-2)=4(x+3)

  7. Put in Point Slope Form • Use point slope form of the equation • Substitute for m, • Solve for y • Slope=-3, Point (-2,4)

  8. Try Another • Slope=-4, Point (-6, -4)

  9. Basic Review • Find the slope of the line and write the equation of the line in point slope form • (-6,3) and (2,-7) • Use the slope formula and the coordinates of the two points to find the slope • Use this slope and one of the given points to write the equation of the line

  10. Try Another • (-9,-2) and (1, -8)

  11. Converting • You can convert from one form of the equation to another by rearranging terms algebraically to match the general form of the line you are looking for.

  12. Put in slope intercept form • 2y=4x+2

  13. 5y=10x+15

  14. 2y+26=-6x

  15. Converting Point Slope to Slope Intercept • The rules are the same • Isolate y on the left hand side of the equation • Slope Intercept is really just the simplified form of point slope

  16. Convert y-2= (x+6)

  17. A little more difficult • Write the equation of a line with a slope of ½ that goes through (2,3) • Easiest to write in which form first? • Do that, then convert algebraically

  18. Try it! • Slope of 10, line passing through (3, 34) • Put in slope intercept form

  19. At your seat! • Convert to slope intercept form • -3y=-9x-12 • Slope of -1 passes through (6,2) • Slope of 0, passes through (7,5)

  20. Converted from point slope to slope intercept • You also converted from general form to slope intercept as well. • More commonly known as standard form but with one small change

  21. Standard Form • Ax+By=C • Common form of a linear equation, however, putting in general form is much easier for picking out key information What is this general form you ask?!!??

  22. General Form • Ax+By+C=0 • X intercept=-C/A • Y intercept=-C/B • Slope=-A/B • How did we figure that out? • By converting from general form to slope intercept!

  23. First, Practice! • X intercept, Y intercept

  24. Converting Forms • Again, really just involves rearranging equations using algebraic operations. • Look at converting to slope intercept first

  25. General Form to Slope Intercept • Goal: Isolate y on one side of an equation • Convert by performing inverse operations on the variable terms and constant terms until y stands alone

  26. Convert 6y+4x-7=0

  27. Converting point slope to general form • Goal: place x and y on one side of the equation with the constant term on the other side. • Move the constant term to the left hand side of the equation, making the right hand side 0. • If any coefficients are fractions, multiply entire equation by the least common denominator of all the fractions.

  28. Convert y+1=(x-2) to general form

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