Linear FunctionsForms of Linear Equations

Standard Form

Linear FunctionsForms of linear equations Information and Definitions

Order Pair Notations: (x, y)

more than one point (x1, y1), (x2, y2), (x3, y3), …(xn, yn)

Variable representation:

m = slope, constant rate of change, gradient, and the following:rise change in y delta y ∆ yrun change in x delta x ∆ x

b = y-intercept, (0, y)

x-intercept = (x, 0)

A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero

Linear FunctionsForms of linear equations Information and Definitions

Standard Form: Ax + By = C3x + 4y = 17; Graph using the x and y intercepts

x-intercept = (17/3 , 0) ; y-intercept = (0, 17/4)

Slope Intercept Form: y = mx + by = 3x + 5; Graph using the y-intercept and the slope

b = 5; m = 3

Point Slope Form: y - y1 = m(x - x1)

y - 4 = 3(x -5); Graph using the point and the gradient

point = (5,4); m = 3

Slope equation: m = y2 - y1

x2- x1

Forms of linear equations Standard Form: Ax + By = C

Write in Standard FormGiven A, B, C

A= 3; B=1; C=12

Standard FormAx + By = C3x + 1y = 12

A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero.

Find x and y interceptsStandard Form: Ax + By = C

3x + y = 12

x-intercept y = 0 y-intercept x = 0 3x + 0 = 12 3(0) + y = 12 3x = 12 x = 4 y=12 (4,0) (0,12)x-intercept y-intercept

x-intercept = (4, 0)y-intercept = (0, 12)

Forms of linear equations Standard Form: Ax + By = C

Write in Standard FormGiven A, B, C

A= 3; B=1; C=12

Standard FormAx + By = C3x + 1y = 12

A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero.

Graph Ax + Bx = CStandard Form: Ax + By = C

3x + y = 12Graph using the x-intercept and y-intercept

x-intercept = (12/3 , 0) = (4, 0)y-intercept = (0, 12/1) = (0, 12)

3x + y = 12

Forms of linear equations Standard Form: Ax + By = C

Write in Standard FormGiven Any Linear Equation

4x = -3y -3

Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below *

4x = -3y -3 Original equation

4x + 3y = -3 Add 3y to both sides

Identify A, B, C: A=4; B=3; C=-3

Satisfies the criteria* below

*A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero.

Find x and y interceptsStandard Form: Ax + By = C

4x + 3y = -3

x-intercept y = 0 y-intercept x = 0 4x + 3(0) = -3 4(0) + 3y = -3 4x = -3 3y = -3 x = -¾ = -.75 y=-3/1 = -1 (-.75,0) (0,-1) x-intercept y-intercept

x-intercept = (-.75, 0)y-intercept = (0, -1)

Forms of linear equations Standard Form: Ax + By = C

Write in Standard FormGiven Any Linear Equation

4x = -3y -3

Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below *

4x = -3y -3 Original equation

4x + 3y = -3 Add 3y to both sides

Identify A, B, C: A=4; B=3; C=-3

Satisfies the criteria* below

*A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero.

Graph Ax + Bx = CStandard Form: Ax + By = C

4x + 3y = -3Graph using the x and y intercepts

x-intercept = (-3/4 , 0) = (-.75, 0)y-intercept = (0, -3/3) = (0, -1)

Forms of linear equations Standard Form: Ax + By = C

Write in Standard FormGiven Slope Intercept Form

y = 7x + 3

Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below *

y = 7x + 3 Original equation

-7x + y = 3 Subtract 7x from both sides(A is not >= 0)

7x - y = -3 Multiply both sides by -1

Identify A, B, C: A=7; B=-1; C=-3

Satisfies the criteria* below

*A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero.

Find x and y interceptsStandard Form: Ax + By = C

7x - y = -3

x-intercept y = 0 y-intercept x = 0 7x - 0 = -3 7(0) - y = -3 7x = -3 -y = -3

x = -3/7 y = 3 (-3/7,0) (0,3) x-intercept y-intercept

x-intercept = (-3/7 , 0)y-intercept = (0, 3)

Forms of linear equations Standard Form: Ax + By = C

Write in Standard FormGiven Slope Intercept Form

y = 7x + 3

Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below *

y = 7x + 3 Original equation

-7x + y = 3 Subtract 7x from both sides(A is not >= 0)

7x - y = -3 Multiply both sides by -1

Identify A, B, C: A=7; B=-1; C=-3

Satisfies the criteria* below

*A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero.

Graph Ax + Bx = CStandard Form: Ax + By = C

7x - y = -3Graph using the x and y intercepts

x-intercept =(-3/7, 0)y-intercept = (0, 3)

Forms of linear equations Standard Form: Ax + By = C

Write in Standard FormGiven Slope Intercept Form

y = -4/9x + 6

Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below *

y = -4/9x + 6 Original equation

4/9x + y = 6 Add 4/9x to both sides(A is not an Integer)

4x + 9y = 54 Multiply both sides by 9

Identify A, B, C: A=4; B=9; C=54

Satisfies the criteria* below

*A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero.

Find x and y interceptsStandard Form: Ax + By = C

4x + 9y = 54

x-intercept y = 0 y-intercept x = 0 4x + 9(0) = 54 4(0) + 9y = 54 4x = 54 9y = 54

x = 54/4 = 13.5 y = 54/9 = 6 (13.5,0) (0,6) x-intercept y-intercept

x-intercept = (13.5, 0)y-intercept = (0, 6)

Forms of linear equations Standard Form: Ax + By = C

Write in Standard FormGiven Slope Intercept Form

y = -4/9x + 6

Get the x and y terms on the same side by themselves Ax + By = C must also satisfy the criteria below *

y = -4/9x + 6 Original equation

4/9x + y = 6 Add 4/9x to both sides(A is not an Integer)

4x + 9y = 54 Multiply both sides by 9

Identify A, B, C: A=4; B=9; C=54

Satisfies the criteria* below

*A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero.

Graph Ax + Bx = CStandard Form: Ax + By = C

4x + 9y = 54Graph using the x and y intercepts

x-intercept = (54/4 , 0) = (13.5, 0)y-intercept = (0, 54/9) = (0, 6)

Linear FunctionsForms of linear equations Information and Definitions

Order Pair Notations: (x, y)

more than one point (x1, y1), (x2, y2), (x3, y3), …(xn, yn)

Variable representation:

m = slope, constant rate of change, gradient, and the following:rise change in y delta y ∆ yrun change in x delta x ∆ x

b = y-intercept, (0, y)

x-intercept = (x, 0)

A, B, C are integers with a GCF of one, where A is greater than or equal to zero and A and B are not both zero

Linear FunctionsForms of linear equations Information and Definitions

Standard Form: Ax + By = C3x + 4y = 17; Graph using the x and y intercepts

x-intercept = (17/3 , 0) ; y-intercept = (0, 17/4)

Slope Intercept Form: y = mx + by = 3x + 5; Graph using the y-intercept and the slope

b = 5; m = 3

Point Slope Form: y - y1 = m(x - x1)

y - 4 = 3(x -5); Graph using the point and the gradient

point = (5,4); m = 3

Slope equation: m = y2 - y1

x2- x1

Linear FunctionsForms of Linear Equations

Standard Form