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# 3 Types of Linear Equations

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by

Tweet## Jaclyn, Megan, and Olivia

on 26 March 2013#### Transcript of 3 Types of Linear Equations

Standard Form Form: ax+by=c

1) You will be given two points, {(x,y),(x,y)}

2) Subtract to get the slope

3) Plug the slope in, and one point into point-slope form: Y-Y =m(X-X ) m=slope

4) Distribute

5) Subtract or add one constant over to the other side of the equation, so you would have slope-intercept form(y=)

6) Add or subtract the x-value to the opposite side of the equation of where it is

7)You would have a standard form equation, if you follow the steps above

8) If you have a fraction, then you need to multiply each number, or value by the denominator of the fraction, because you cannot have fractions in standard form The Three Types of

Linear Equations Then... First... To Finish...

4) Y-4 = 3/4X - 3/4

5) Y-4 = 3/4X - 3/4

+4 +4

6) Y = 3/4X + 13/4

-3/4X -3/4X

7) -3/4X + Y = 13/4

8) -3/4X(4) + Y(4) = 13/4(4)

9) -3X + 4Y = 13

*Number 9 is in standard form Slope-Intercept Form Part I: Step 1) With your two given points, {(x,y), (x,y)},

calculate the slope. Use: y = mx + b slope y-intercept Step 2) With the slope and one of the given points,

plug it into y = mx + b form to find b, the

y-intercept. Step 3) Solve the equation that you have just made. 1. Multiply the slope by the x value.

2. Rewrite

3. Add or subtract the value to "get rid of itself"

and to the other side of the equation.

4. You should come out with a number equals b,

and this id your y-intercept. Step 4) Write the equation in y = mx + b form with

the slope you found and the y-intercept. Part II: Part III: 5) That's it. You should have your finished

equation. Now for an Example: Use the two given points to find the equation

in slope-intercept form. (3,5),(4,6) Step 1) 6—5 ______ 4—3 m= = -1 ___ 1 = -1 Step 2) y = mx + b (3,5) 5 = -1( 3 ) + b 5 = -3 + b +3 +3 ______________ 8 = b Step 3) Step 4) y = mx + b y = -1x + 8 Step 5) *Or, (because the slope is one), you do not have to include the -1 so you could also do...* y = -x + 8 by Jaclyn Steps 4-7 Last Steps! 1 1 Use the two points to find an equation of the line. The equation should be in standard form. (1,4),(5,7) 7 - 4 m= = 3 y 1 *Plug into the formula* y 3 4 Step 1) Step 2) Step 3) y 3 4 x 3 4 +4 +4 _____________ y Step 4) 3 ___ 4 x 13 ___ 4 -3 ___ 4 x - 3 ___ 4 ________________ Step 5) Step 6) ¾ ¾ -3 ___ 4 x + = 13 ____ 4 Step 7) Step 8) (4) (4) (4) *Don't forget to multiply by

the common denominator to

eliminate the fractions.* Step 9) ______________ -3x And now... The moment you've all been waiting for! POINT SLOPE POINT SLOPE POINT SLOPE by Olivia The

Equation

is y1 being the y in your first coordinate x1 being the x in your first coordinate m being the slope y-y1=m(x-x1) How to solve! Given 2 points (x,y) and (x,y),

find the slope using Plug in the , and into

the point slope formula y-y1=m(x-x1) AND ITS COMPLETE! Step 1) Step 2) slope y1 x1 (unless you have to simplify

it to slope intercept) Now for an

EXAMPLE Use the points (6,-2) and (3,1) to write an

equation in Point Slope form Step 1) Find the slope using (6,-2) and (3,1) m= y2-y1

x2-x1 1-(-2)

3-6 = = 3

-3 =-1 Step 2) Plug the slope, y1 and x1 into y-y1=x-x1 y-(-2)=-1(x-6) And That's all! by Megan Megan explains in 5

easy steps! Don't forget to

circle it! Yeah, yeah we

get it. Olivia

is up next. Steps: Example: ______ 5 - 1 __ y 1 = ( x - ) = __ ( x 1 ) - __ - x y + 4y = 13 After that you are DONE YAY! x 4 m - 4 4 - __ - = - =

Full transcript1) You will be given two points, {(x,y),(x,y)}

2) Subtract to get the slope

3) Plug the slope in, and one point into point-slope form: Y-Y =m(X-X ) m=slope

4) Distribute

5) Subtract or add one constant over to the other side of the equation, so you would have slope-intercept form(y=)

6) Add or subtract the x-value to the opposite side of the equation of where it is

7)You would have a standard form equation, if you follow the steps above

8) If you have a fraction, then you need to multiply each number, or value by the denominator of the fraction, because you cannot have fractions in standard form The Three Types of

Linear Equations Then... First... To Finish...

4) Y-4 = 3/4X - 3/4

5) Y-4 = 3/4X - 3/4

+4 +4

6) Y = 3/4X + 13/4

-3/4X -3/4X

7) -3/4X + Y = 13/4

8) -3/4X(4) + Y(4) = 13/4(4)

9) -3X + 4Y = 13

*Number 9 is in standard form Slope-Intercept Form Part I: Step 1) With your two given points, {(x,y), (x,y)},

calculate the slope. Use: y = mx + b slope y-intercept Step 2) With the slope and one of the given points,

plug it into y = mx + b form to find b, the

y-intercept. Step 3) Solve the equation that you have just made. 1. Multiply the slope by the x value.

2. Rewrite

3. Add or subtract the value to "get rid of itself"

and to the other side of the equation.

4. You should come out with a number equals b,

and this id your y-intercept. Step 4) Write the equation in y = mx + b form with

the slope you found and the y-intercept. Part II: Part III: 5) That's it. You should have your finished

equation. Now for an Example: Use the two given points to find the equation

in slope-intercept form. (3,5),(4,6) Step 1) 6—5 ______ 4—3 m= = -1 ___ 1 = -1 Step 2) y = mx + b (3,5) 5 = -1( 3 ) + b 5 = -3 + b +3 +3 ______________ 8 = b Step 3) Step 4) y = mx + b y = -1x + 8 Step 5) *Or, (because the slope is one), you do not have to include the -1 so you could also do...* y = -x + 8 by Jaclyn Steps 4-7 Last Steps! 1 1 Use the two points to find an equation of the line. The equation should be in standard form. (1,4),(5,7) 7 - 4 m= = 3 y 1 *Plug into the formula* y 3 4 Step 1) Step 2) Step 3) y 3 4 x 3 4 +4 +4 _____________ y Step 4) 3 ___ 4 x 13 ___ 4 -3 ___ 4 x - 3 ___ 4 ________________ Step 5) Step 6) ¾ ¾ -3 ___ 4 x + = 13 ____ 4 Step 7) Step 8) (4) (4) (4) *Don't forget to multiply by

the common denominator to

eliminate the fractions.* Step 9) ______________ -3x And now... The moment you've all been waiting for! POINT SLOPE POINT SLOPE POINT SLOPE by Olivia The

Equation

is y1 being the y in your first coordinate x1 being the x in your first coordinate m being the slope y-y1=m(x-x1) How to solve! Given 2 points (x,y) and (x,y),

find the slope using Plug in the , and into

the point slope formula y-y1=m(x-x1) AND ITS COMPLETE! Step 1) Step 2) slope y1 x1 (unless you have to simplify

it to slope intercept) Now for an

EXAMPLE Use the points (6,-2) and (3,1) to write an

equation in Point Slope form Step 1) Find the slope using (6,-2) and (3,1) m= y2-y1

x2-x1 1-(-2)

3-6 = = 3

-3 =-1 Step 2) Plug the slope, y1 and x1 into y-y1=x-x1 y-(-2)=-1(x-6) And That's all! by Megan Megan explains in 5

easy steps! Don't forget to

circle it! Yeah, yeah we

get it. Olivia

is up next. Steps: Example: ______ 5 - 1 __ y 1 = ( x - ) = __ ( x 1 ) - __ - x y + 4y = 13 After that you are DONE YAY! x 4 m - 4 4 - __ - = - =