SOLUTION: Can you help me please? How can you determine if 8x=6y+7 as a linear equation with two variables? Is the equation a linear equation in two variables?

Question 632927: Can you help me please? How can you determine if 8x=6y+7 as a linear equation with two variables? Is the equation a linear equation in two variables?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
8x = 6y + 7 is a linear equation in 2 variables.
you have 2 variables, x and y.
the highest exponent for any variable in the equation is 1.
note that x is equivalent to x^1 and y is equivalent to y^1.
to convert this equation to standard form of a linear equation, subtract 6y from both sides of the equation to get:
8x - 6y = 7
to convert this equation to slope intercept form of a linear equation, subtract 8x from both sides of the equation to get:
-6y = -8x + 7
multiply both sides of this equation by -1 to get:
6y = 8x - 7
divide both sides of this equation by 6 to get:
y = (8x-7)/6 which is then simplified to:
y = (8/6)x - (7/6) which is then further simplified to:
y = (4/3)x - (7/6)
an equation is linear if the highest exponent of any term in the equation is equal to 1.
note that we are talking about a polynomial equation which requires that all exponents not be negative and be integers.
under these rules, x^0 is the lowest exponent that can be used.
note that x^0 = 1
some linear equations under these rules are:
y = 5 (exponent of y is 1 and 5 is a constant)
x = 5 (exponent of x is 1 and 5 is a constant)
y = 5x (exponent of x is 1 and exponent of y is 1)
y = 5x - 13 (exponent of x is 1 and exponent of y is 1 and -13 is a constant)

note that y = 5x could also be written as -5x + y = 0 and could also be written as 5x = y
note that y = 5x - 13 could also be written as -5x + y = -13 and could also be written as -5x = -y - 13

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