Graphing Linear Relationships

a

An equation written in standard form follows the format

A x + B y = C

where

A,

B,

and

C

are real numbers. It's also worth noting that

A

and

B

cannot both be zero. To rewrite the given equation in standard form with integer coefficients, we need to isolate the constant on the right-hand side of the equation.

y + 5 = 3 (x - 2)

DistrDistribute

3

y + 5 = 3 x - 6

SubEqn

LHS - 5 = RHS - 5

y = 3 x - 11

SubEqn

LHS - 3 x = RHS - 3 x

y - 3 x = - 11

CommutativePropAddCommutative Property of Addition

- 3 x + y = - 11

Now we can see that our equation follows the standard form.

A x - 3 x + + B y, y = C = 11

b

To rewrite the given equation in standard form with integer coefficients, we need to isolate the constant on the right-hand side of the equation. To get rid of the fraction, we need to multiply both sides by its denominator.

y = - \frac{3}{4} x - 3.5

MultEqn

LHS \cdot 4 = RHS \cdot 4

4 y = 4 (- \frac{3}{4} x - 3.5)

DistrDistribute

4

4 y = - 3 x - 14

AddEqn

LHS + 3 x = RHS + 3 x

4 y + 3 x = - 14

CommutativePropAddCommutative Property of Addition

3 x + 4 y = - 14

Now we can see that our equation follows the standard form.

A x 3 x + + B y 4 y = C = - 14

Graphing Linear Relationships 1.4 - Solution