Determine the equation of a line which passes through a point (2,-3) and is parallel to another line 3x-6y+7=0.

We know that 2 lines are parallel if the values of their slopes are equal.

The given equation is 3x-6y+7=0 and we have to write in the standard from, which is y = mx+n.

We'll isolate y to the left side:

-6y = -3x-7

We'll divide by -6:

y = (1/2)x + 7/6

So, the slope can be easily determined as m1 = 1/2.

That means that the second slope has the same value:

m2 = 1/2

The line which passes through the point (2,-3) and has the slope m2 = 1/2 has the equation:

y+3 = (1/2)(x-2)

We'll open the brackets:

y+3 = x/2 -1

We'll add -3 both sides:

y = x/2 -1 - 3

The equation of the parallel line, which passes through (2,-3) is:

y = x/2 - 4