Video Transcript
A straight line ๐ฟ has the equation
๐ฆ equals negative two ๐ฅ minus three. Find the equation of the line
parallel to ๐ฟ that passes through the point one, three.
Parallel lines will have have the
exact same slope, so the line ๐ฟ has a slope of negative two. That means the parallel line to ๐ฟ
will also have to have a slope of negative two. And we also know that that parallel
line needs to go through the point one, three. So we have the slope and we have a
point that it should go through. So we can actually use the point
slope formula and this will help us find the equation of this line.
So the point one, three will be
substituted in for ๐ฅ one and ๐ฆ one. And negative two will be
substituted in for m. So we have ๐ฆ minus three equals
negative two times ๐ฅ minus one. Now we need to put it in the form
๐ฆ equals ๐๐ฅ plus ๐, so we need to isolate ๐ฆ. So first on the right-hand side,
letโs use the distributive property. ๐ฆ minus three equals negative two
๐ฅ plus two. And then to solve for ๐ฆ, we need
to add three to both sides and doing so we get the equation ๐ฆ equals negative two
๐ฅ plus five. This would be the line thatโs
parallel to ๐ฟ that passes through the point one, three.
