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: (-3,-4);2y=4+3x , (5,-1);y=-3/5x-3 , (9,4);y-x=3...
You are allowed to ask only one question at a time, I have edited your question to comply with the same.
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.