You can put this solution on YOUR website! Given a linear equation in any form, any line with an equation that has the same coefficients as the given equation on the x and y terms is parallel to the given line.
In your example, the given equation is
Any other linear equation with the same coefficients on the x and y terms will have a graph that is parallel to the graph of the given line. So the lines
are all parallel to your given line.
To find the equation of the line in your problem, simply plug in the x and y values of the given point and solve for the constant term:
So the constant term in the equation you are looking for is 22; and then the full equation is
The concept is also applicable if the given linear equation is in a different form. If, for example, you are given the equation
and you want an equation of the line parallel to that given line and passing through the point (6,1), then you know the equation can be in the form
where n is some constant to be determined; and you can determine that constant by plugging in the coordinates of the given point.
and so the desired equation is
