Question

1. convert the point - slope form $y + 3 = 2(x - 1)$ to standard form.

a. $x - 2y = 5$
b. $x - 2y = 1$
c. $2x + y = 5$
d. $2x - y = 5$

Explanation:

Step1: Expand the right - hand side

We start with the point - slope form \(y + 3=2(x - 1)\). First, we use the distributive property \(a(b - c)=ab - ac\) (here \(a = 2\), \(b=x\), \(c = 1\)) to expand the right - hand side. So \(y+3 = 2x-2\).

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 \(y\) from both sides: \(3=2x - y-2\). Then add 2 to both sides: \(2x-y=5\).

Answer:

d. \(2x - y = 5\)