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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.
In slope-Intercept form, that passes through the given point and is perpendicular* to the given line.
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