Question

what is $y - 2 = -3(x - 7)$ written in standard form? choose 1 answer: a $3x + y - 23 = 0$ b $y = -3x + 23$ c $3x + y = 23$ d $y - 2 = -3x + 21$

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 \(A\geq0\).

Step2: Expand the given equation

Start with \(y - 2 = -3(x - 7)\). Expand the right - hand side: \(y - 2=-3x + 21\) (using the distributive property \(a(b - c)=ab - ac\), here \(a=-3\), \(b = x\), \(c = 7\)).

Step3: Rearrange the equation to standard form

Add \(3x\) to both sides of the equation \(y - 2=-3x + 21\):
\(3x+y - 2=21\)
Then add 2 to both sides:
\(3x + y=21 + 2\)
\(3x + y=23\)

Answer:

C. \(3x + y = 23\)