Question

write an equation of the line that is parallel to the given line and passes through the given point.
y=-4x-7, (5,-3)
y=-2/3x+4, (-5,5)

Answer 1

First, from a given line, the slope can be identified if the equation of the line is put into the slope-intercept form as:
y = mx + b

For example,
2x + 3y = 5 can be rearranged to
y = (-2/3)x + 5/3
From which we can identify the slope as (-2/3).

One the slope is defined, if the line is to pass through a given point with coordinates (x1,y1), the equation of the line sought is:

y = m(x-x1) + y1

So if a line parallel to the above line is to pass through (3,2), the equation would be:
y = (-2/3)(x - 3) + 2, or
y = (-2/3)x + 4