Question

convert the point - slope form $y + 3 = 2(x - 1)$ to standard form.
a. $x - 2y = 5$
b. $2x + y = 5$
c. $x - 2y = 1$
d. $2x - y = 5$

Explanation:

Step1: Expand the right - hand side

We start with the equation \(y + 3=2(x - 1)\). Using the distributive property \(a(b - c)=ab - ac\), where \(a = 2\), \(b=x\) and \(c = 1\), we get \(y+3 = 2x-2\).

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

We want to move all the \(x\) and \(y\) terms to one side and the constant to the other. Subtract \(y\) from both sides and add 2 to both sides.
From \(y + 3=2x-2\), subtract \(y\) from both sides: \(3=2x - y-2\). Then add 2 to both sides: \(2x-y=3 + 2=5\).

Answer:

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