Let's start by tidying up that equation and put it into slope-intercept form (y = mx + b); from there, we can plug in coordinates.
[tex]y - 4 = 3(x-2)[/tex]
Let's use the distributive property on the right side:
[tex]y - 4= 3x - 6[/tex]
Now add 4 to both sides
[tex](y - 4) + 4 = (3x - 6) + 4[/tex]
Which simplifies to:
[tex]y = 3x - 2[/tex]
Since that's the equation of our line, now we can plug in coordinates and see what it churns out.
We know that the x-coordinate of P = 4 so let's substitute 4 in for x and calculate the y-coordinate:
[tex]y = 3(4) - 2[/tex]
[tex]y = 12 - 2[/tex]
[tex]y = 10[/tex]
So the y-coordinate for point P = 10
