Question

what is $y + 3 = 7(x - 2)$ written in standard form? choose 1 answer: a $y = 7x - 5$ b $y = 7x - 17$ c $-7x + y = -5$ d $-7x + y = -17$

Explanation:

Step1: Expand the right - hand side

The given equation is \(y + 3=7(x - 2)\). First, we use the distributive property \(a(b - c)=ab - ac\) (here \(a = 7\), \(b=x\), \(c = 2\)) to expand the right - hand side. So \(7(x - 2)=7x-14\). The equation becomes \(y + 3=7x-14\).

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 the left - hand side and the constant on the right - hand side. Subtract \(7x\) from both sides: \(y+3 - 7x=7x-14 - 7x\), which simplifies to \(-7x + y+3=-14\). Then subtract 3 from both sides: \(-7x + y+3 - 3=-14 - 3\), so \(-7x + y=-17\).

Answer:

D. \(-7x + y=-17\)