Exercise 29 Page 234

Practice makes perfect

We are asked to change the given equation into the y=mx+b form. y-4x=-3 To do so, we will solve equation for y by using the Properties of Equality to apply inverse operations to the equation.

y-4x=-3

AddEqn

LHS+4x=RHS+4x

y-4x+4x=-3+4x

\AddTerm

y=- 3 +4x

CommutativePropAdd

Commutative Property of Addition

y=4x-3

We will change the following equation into y=mx+b form. 3y-3x=9 To do this, we will solve this equation for y. Let's use the Properties of Equality to apply inverse operations on the equation.

3y-3x=9

AddEqn

LHS+3x=RHS+3x

3y-3x+3x=9+3x

AddTerms

Add terms

3y=9+3x

CommutativePropAdd

Commutative Property of Addition

3y=3x+9

DivEqn

.LHS /3.=.RHS /3.

3y/3=3x+9/3

WriteSumFrac

Write as a sum of fractions

3y/3=3x/3+9/3

MoveRightFacToNum

a/c* b = a* b/c

3/3y=3/3x+9/3

CalcQuot

Calculate quotient

1y=1x+3

IdPropMult

Identity Property of Multiplication

y=x+3

We will change the following equation into y=mx+b form. 3x+2y=12 We can do this by solving this equation for y. Let's use the Properties of Equality to apply inverse operations on the equation.

3x+2y=12

SubEqn

LHS-3x=RHS-3x

3x-3x+2y=12-3x

SubTerm

Subtract term

2y=12-3x

CommutativePropAdd

Commutative Property of Addition

2y=- 3x+12

DivEqn

.LHS /2.=.RHS /2.

2y/2=- 3x+12/2

WriteSumFrac

Write as a sum of fractions

2y/2=- 3x/2+12/2

MoveRightFacToNum

a/c* b = a* b/c

2/2y=- 3/2x+12/2

CalcQuot

Calculate quotient

1y=- 3/2x+6

IdPropMult

Identity Property of Multiplication

y=- 3/2x+6

MoveNegNumToFrac

Put minus sign in front of fraction

y=- 3/2x+6

We are asked to change the following equation into y=mx+b form. 2(x-3)+3y=0 To do this we can use Properties of Equality to solve this equation for y. Let's start by using the Distributive Property to simplify the left-hand side of the equation.

2(x-3)+3y=0

Distr

Distribute 2

2x-2(3)+3y=0

Multiply

2x-6+3y=0

SubEqn

LHS-2x=RHS-2x

2x-2x-6+3y=- 2x

AddEqn

LHS+6=RHS+6

2x-2x-6+6+3y=- 2x+6