Question 1093119
<br>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.<br>
In your example, the given equation is
{{{y = 4x+7}}}<br>
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
{{{y = 4x+10}}}
{{{y = 4x-3}}}
{{{y = 4x-39023}}}
are all parallel to your given line.<br>
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:
{{{y = 4x+b}}}
{{{10 = 4(-3)+b}}}
{{{10 = -12+b}}}
{{{22 = b}}}<br>
So the constant term in the equation you are looking for is 22; and then the full equation is
{{{y = 4x+22}}}<br>
The concept is also applicable if the given linear equation is in a different form.  If, for example, you are given the equation
{{{2x-5y = 9}}}
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
{{{2x-5y = n}}}
where n is some constant to be determined; and you can determine that constant by plugging in the coordinates of the given point.
{{{2x-5y = n}}}
{{{2(6)-5(1) = 12-5 = 7}}}
and so the desired equation is
{{{2x-5y = 7}}}