y=56x+526

The standard form of a linear equation is Ax+By=C.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

6,26

Since 6,26 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 6,26 then find LCM for the variable part .

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

6 has factors of 2 and 3.

2⋅3

26 has factors of 2 and 13.

2⋅13

The LCM of 6,26 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2⋅3⋅13

The LCM of 6,26 is 2⋅3⋅13=78.

Multiply 2 by 3.

6⋅13

Multiply 6 by 13.

78

78

78

Multiply both sides by 78.

78y=78(56x+526)

Combine 56 and x.

78y=78(5×6+526)

Apply the distributive property.

78y=785×6+78(526)

Cancel the common factor of 6.

Factor 6 out of 78.

78y=6(13)5×6+78(526)

Cancel the common factor.

78y=6⋅135×6+78(526)

Rewrite the expression.

78y=13(5x)+78(526)

78y=13(5x)+78(526)

Multiply 5 by 13.

78y=65x+78(526)

Cancel the common factor of 26.

Factor 26 out of 78.

78y=65x+26(3)526

Cancel the common factor.

78y=65x+26⋅3526

Rewrite the expression.

78y=65x+3⋅5

78y=65x+3⋅5

Multiply 3 by 5.

78y=65x+15

78y=65x+15

Rewrite the equation with the sides flipped.

65x+15=78y

Subtract 78y from both sides of the equation.

65x+15-78y=0

Move 15.

65x-78y+15=0

65x-78y+15=0

Subtract 15 from both sides of the equation.

65x-78y=-15

Rewrite in Standard Form y=5/6x+5/26