Video: Finding the Equation of a Line Parallel to a Given Line

Video Transcript

A straight line 𝐿 has the equation 𝑦 equals negative two 𝑥 minus three. Find the equation of the line parallel to 𝐿 that passes through the point one, three.

Parallel lines will have have the exact same slope, so the line 𝐿 has a slope of negative two. That means the parallel line to 𝐿 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 𝑥 one and 𝑦 one. And negative two will be substituted in for m. So we have 𝑦 minus three equals negative two times 𝑥 minus one. Now we need to put it in the form 𝑦 equals 𝑚𝑥 plus 𝑏, so we need to isolate 𝑦. So first on the right-hand side, let’s use the distributive property. 𝑦 minus three equals negative two 𝑥 plus two. And then to solve for 𝑦, we need to add three to both sides and doing so we get the equation 𝑦 equals negative two 𝑥 plus five. This would be the line that’s parallel to 𝐿 that passes through the point one, three.