The equation [tex]$y-2=3(x+1)$[/tex] is in point-slope form. Which is the slope-intercept form?

A. [tex]$y=3x+1$[/tex]
B. [tex][tex]$y=3x-3$[/tex][/tex]
C. [tex]$y=3x+5$[/tex]



Answer :

To convert the given point-slope form equation [tex]\( y - 2 = 3(x + 1) \)[/tex] into slope-intercept form (which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept), follow these steps:

1. Distribute the 3 on the right-hand side:
[tex]\[ y - 2 = 3x + 3 \][/tex]

2. Isolate [tex]\( y \)[/tex] by adding 2 to both sides of the equation:
[tex]\[ y - 2 + 2 = 3x + 3 + 2 \][/tex]
Simplifying the left side, we get:
[tex]\[ y = 3x + 5 \][/tex]

Now, the equation is in slope-intercept form. Therefore, the slope-intercept form of the equation is:

[tex]\[ y = 3x + 5 \][/tex]

The correct answer is:

[tex]\[ y = 3x + 5 \][/tex]