What is the equation of the line in slope-intercept form, that passes through a given point and which is parallel to a given line. For example:...

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Any problem
where you want to find the equation of a line in slope-intercept form which is parallel
to a given line and which passes through a given point can be solved in the following
way.

Let the point that is given be (a1, b1) and let the
line be y = mx + c

As two parallel lines have the same
slope the line you get will have the slope m. The line also has to pass through (a1,
b1). It can be written as: (y - b1)/(x - a1) = m

=>
y - b1 = mx - m*a1

=> y = mx + ( b1 -
m*a1)

This is the equation of the line in slope-intercept
form that passes through (a1, b1) and is parallel to y = mx +
c.

In the problems you are given substitute the values of
m, a1 and b1  you get the required equation.