When y-1=-4/5(x-3) is written in standard form using positive integers, what is the smallest possible coeficcient of x?
y-1=-4/5(x-3)
5y - 5 = -4x + 12
4x + 5y - 17 = 0
> ... what is the smallest possible coeficcient of x >
clearly the coefficient of the x term is 4
why would you want it anything other than that?
how did you get 5y-5 on the left side?
To write the equation y - 1 = -4/5(x - 3) in standard form using positive integers, we need to multiply through by the denominators to eliminate any fractions.
First, let's distribute -4/5 to the terms inside the parentheses, which gives us y - 1 = -4/5*x + 12/5.
Next, we can move the x term to the left side of the equation and the constant term to the right side to get -4/5*x - y = 1 - 12/5.
Now, let's find a common denominator for the constant terms on the right side of the equation. The common denominator for 1 and 12/5 is 5.
Converting 1 to 5/5, we get -4/5*x - y = 5/5 - 12/5. Simplifying the right side, we have -4/5*x - y = -7/5.
To eliminate the fractions, we can multiply through by the common denominator of 5. This gives us -4x - 5y = -7.
Now, the standard form of the equation is Ax + By = C, where A, B, and C are positive integers. However, the question asks for the smallest possible coefficient of x, so we can multiply the equation by -1 to get 4x + 5y = 7.
Therefore, the smallest possible coefficient of x in the standard form of the given equation is 4.