for the line that passes through the point (4,2) and is parallel to the line whose equation is
y = x/3 - 1
being parallel means to have the exact same slope, therefore in the format y = mx + b, the slope (m) is 1/3
so now we need the line that has a slope of 1/3 and passes thru (4, 2)
we'll use the "point-slope" format for this:
[tex]y - y1 = m \: (x - x1) \\ where \: the \: point \: is \: (x1.y1) \\ y - 2 = 1/3 \: (x - 4) \\ [/tex]
now solve for y:
[tex]y - 2 + 2= 1/3 \: (x - 4) + 2\\ y = 1/3x - 4/3 + 2 \\ solve \: for \: common \: denominator \\ of \: 3[/tex]
[tex]y = 1/3x - 4/3 + 2 \\ y= 1/3x - 4/3 + 6/3 \\ y = 1/3x + 2/3[/tex]
THEREFORE C) y = 3x - 2/3
IS THE CORRECT ANSWER!
