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M. Pickens 2006 Slope Intercept form and Solving for y

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M. Pickens 2006 Objectives To learn what slope intercept form is To practice identifying slope and y-intercept when in slope-intercept form To practice solving equations for y to put in slope intercept form.

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M. Pickens 2006 What is Slope Intercept Form? Slope-Intercept Form is a way to write the equation of a line. Slope Intercept form is : m is the slope b is the y-intercept

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M. Pickens 2006 Identify the Slope and Y-intercept y = 2x + 5 SlopeSlope = 2Y-intercept Y-intercept = 5 Slope =Y-intercept =-2

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M. Pickens 2006 Identify the Slope and Y-intercept SlopeY-intercept Slope = Y-intercept = Slope = Y-intercept =0 + 0 Slope = Y-intercept =-9

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M. Pickens 2006 Solving for Y Often an equation is not in slope-intercept form. To get it in slope intercept form solve for y first. Example: 4x + 2y = 9 We are trying to get the y by itself. First we can move the 4x by subtracting 4x from both sides -4x We cant combine the 9 and -4x because they are not like terms 2y = 9 – 4x Now we can cancel out the *2 by dividing both sides by 2. To do this we will have to divide each piece by 2 2 2 2 y = 4.5 – 2x Now put in slope-intercept form y = -2x + 4.5

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M. Pickens 2006 Solving for Y Put in slope-intercept form then give the slope and y-intercept 3y + 2 = 3x - 5 We are trying to get the y by itself. First we can move the 2 by subtracting 2 from both sides -2 3y = 3x - 7 Now we can cancel out the *3 by dividing both sides by 3. To do this we will have to divide each piece by 3 3 3 3 y = 1x – 7/3 or y = 1x – 2.3 Slope = 1 Y- int =-7/3 or -2.3

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M. Pickens 2006 Examples 3x + 4y = 8 We are trying to get the y by itself. First we can move the 3x by subtracting 3x from both sides -3x 4y = We cant combine the 8 and -3x as they are not like terms -3x + 8 Now we can cancel out the *4 by dividing both sides by 4. To do this we will have to divide each piece by 4 4 4 4 y =-3/4 x +2 Now it is in slope intercept form. What are the slope and y-intercept? Slope = -3/4 Y- int =2

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M. Pickens 2006 Examples 2y – 5x = -4 We are trying to get the y by itself. First we can move the -5x by adding 5x to each side of the equals +5x +5x 2y = We cant combine the -4 and 5x as they are not like terms 5x – 4 Now we can cancel out the *2 by dividing both sides by 2. To do this we will have to divide each piece by 2 2 2 2 y =5/2 x – 2 Now it is in slope intercept form. What are the slope and y-intercept? Slope = 5/2 or 2.5 Y- int =-2 Or y = 2.5x – 2

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M. Pickens 2006 Examples -1x + 2y = 6 We are trying to get the y by itself. First we can move the -1x by adding 1x to each side of the equals +1x +1x 2y = We cant combine the 6 and 1x as they are not like terms 1x + 6 Now we can cancel out the *2 by dividing both sides by 2. To do this we will have to divide each piece by 2 2 2 2 y =1/2 x + 3 Now it is in slope intercept form. What are the slope and y-intercept? Slope = 1/2 or 0.5 Y- int =3 Or y = 0.5x + 3 -x + 2y = 6

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M. Pickens 2006 Examples 2y + -4x = 2x +7 We are trying to get the y by itself. First we can move the -4x by adding 4x to each side of the equals +4x 2y = 6x +7 Now we can cancel out the *2 by dividing both sides by 2. To do this we will have to divide each piece by 2 2 2 2 y = 3x + 7/2 or y = 3x + 3.5 Slope = 3 Y- int =7/2 or 3.5

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M. Pickens 2006 Conclusion The equation for slope-intercept form is: M = ________________ B = ________________ To get an equation in slope intercept form, first _______________ slope y-intercept solve for y

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Solving Equations with Brackets or Fractions. Single Bracket Solve 3(x + 4) = 24 3x + 12 = 24 3x + 12 – 12 = 24 -12 3x = 12 x = 4 Multiply brackets out.

Solving Equations with Brackets or Fractions. Single Bracket Solve 3(x + 4) = 24 3x + 12 = 24 3x + 12 – 12 = 24 -12 3x = 12 x = 4 Multiply brackets out.

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