Question

the equation $y - 2 = 3(x + 1)$ is in point - slope form. which is the slope - intercept form?
$\square$ $y = 3x + 1$
$\square$ $y = 3x - 3$
$\square$ $y = 3x + 5$
done \checkmark

Explanation:

Step1: Expand the right side

We start with the equation \( y - 2 = 3(x + 1) \). Using the distributive property \( a(b + c)=ab+ac \), we expand the right - hand side: \( y - 2=3x + 3\times1=3x + 3 \).

Step2: Solve for y

To get the equation in slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept), we add 2 to both sides of the equation \( y - 2=3x + 3 \).
Adding 2 to both sides: \( y-2 + 2=3x+3 + 2 \).
Simplifying both sides, we get \( y = 3x+5 \).

Answer:

\( y = 3x + 5 \) (the option with \( y = 3x + 5 \))