Question

write the equation in standard form
$y - 10 = 2(x - 8)$

Explanation:

Step1: Expand the right side

We use the distributive property \(a(b - c)=ab - ac\) to expand \(2(x - 8)\). So \(2(x - 8)=2x-16\). The equation becomes \(y - 10=2x-16\).

Step2: Rearrange to standard form

The standard form of a linear equation is \(Ax + By=C\) (where \(A\), \(B\), and \(C\) are integers, and \(A\geq0\)). We want to get all the \(x\) and \(y\) terms on one side and the constant on the other. Subtract \(2x\) from both sides: \(y-2x - 10=- 16\). Then add 10 to both sides: \(y-2x=-16 + 10\). Simplify the right side: \(y-2x=-6\). We can also write it as \(-2x + y=-6\), but usually we make \(A\) positive, so multiply both sides by \(- 1\) to get \(2x-y = 6\).

Answer:

The standard form of the equation \(y - 10=2(x - 8)\) is \(2x - y=6\) (or equivalent forms like \(-2x + y=-6\) but the form with positive \(x\) coefficient is more standard).