Since any two parallel lines have the same slope we know the slope of the unknown line is (its from the slope of which is also ).
Also since the unknown line goes through (0,3), we can find the equation by plugging in this info into the point-slope formula
Point-Slope Formula:
where m is the slope and (,) is the given point
Plug in , , and
Distribute
Multiply
Add to both sides to isolate y
Make into equivalent fractions with equal denominators
Combine the fractions
Reduce any fractions
So the equation of the line that is parallel to and goes through (,) is
So here are the graphs of the equations and
graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)
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