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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)

  • maths -

    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

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