Question

question 4
write the following equation in standard form.
$y - 3 = 2(x - 1)$

Explanation:

Step1: Expand the right side

We use the distributive property \(a(b - c)=ab - ac\). Here \(a = 2\), \(b=x\), \(c = 1\), so \(2(x - 1)=2x-2\). The equation becomes \(y - 3=2x-2\).

Step2: Rearrange to standard form \(Ax + By=C\)

We want to get all the \(x\), \(y\) terms on one side and the constant on the other. Subtract \(2x\) from both sides and add \(3\) to both sides. \(-2x + y=-2 + 3\), which simplifies to \(-2x + y = 1\). We can also multiply both sides by \(- 1\) to make the \(x\) coefficient positive, getting \(2x-y=-1\) (both forms are correct, but usually the leading coefficient of \(x\) is positive in standard form).

Answer:

\(2x - y=-1\) (or \(-2x + y = 1\))