Question

what is $y = \frac{4}{5}x + 2$ written in standard form? choose 1 answer: a $5y = 4x + 10$ b $-4x + 5y = 10$ c $-\frac{4}{5}x + y - 2 = 0$ d $y = \frac{4}{5}\left(x + \frac{5}{2}\
ight)$

Explanation:

Step1: Recall standard form of a linear equation

The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) is non - negative. The given equation is \(y=\frac{4}{5}x + 2\).

Step2: Eliminate the fraction

Multiply each term in the equation \(y=\frac{4}{5}x + 2\) by 5 to get rid of the fraction.
\(5\times y=5\times\frac{4}{5}x+5\times2\)
\(5y = 4x+10\)

Step3: Rearrange to standard form

Subtract \(4x\) from both sides of the equation \(5y = 4x + 10\) to get it in the form \(Ax+By = C\).
\(- 4x+5y=10\) (Here, we can also write it as \(4x - 5y=- 10\), but the form \(-4x + 5y = 10\) is also a valid standard form as long as \(A\), \(B\), \(C\) are integers. If we want \(A\) to be non - negative, we can multiply both sides by \(- 1\) to get \(4x-5y=-10\), but among the given options, \(-4x + 5y = 10\) is in the standard form structure and is equivalent after re - arrangement)

Answer:

B. \(-4x + 5y = 10\)