 Hey I'm Lucy and in this video we're going to look at how to find the equation of parallel lines. You should already know that straight lines follow the y equals mx plus c format and how to find the gradient but if you've forgotten you may want to watch these two videos first. Parallel lines are found everywhere. You see them on train tracks, sports pictures, rows of seats in a stadium and on a graph they look like this. The lines are all running in the same direction with the same steepness or gradient. Parallel lines have the same gradient and to find the equation of parallel lines we still use the y equals mx plus c equation. Because they have the same gradient we know straight away that the m will be the same. So the equation of this line is y equals 2x plus 6. What are the equation of a parallel line that passes through the point 4 negative 2b? It must have the same gradient because it's parallel so the gradient of both lines is 2. Remembering that the gradient is the number in front of the x in the y equals mx plus c equation so for a parallel line we already know y equals 2x plus c. So now we just need to find the missing y intercept c value. We take the coordinate from the question and substitute it in. So x is 4 and y is negative 2 into the y equals 2x plus c equation and we get negative 2 equals 2 multiplied by 4 plus c. As negative 2 equals 8 plus c little bit of rearranging and c is negative 10. So the equation of the parallel line is y equals 2x minus 10. Your turn now, what is the equation of the line that is parallel to y equals negative 2x plus 5 and passes through the point 1 negative 1. Pause the video, work out the answer and click play when you're ready to check. Did you get y equals negative 2x plus 1? Parallel lines means that the gradient is also negative 2 so we already have y equals negative 2x plus c and we just need to work out the y intercept. Using 1 negative 1 from the question and we substitute in x is 1 and y is negative 1 into our equation we get negative 1 equals negative 2 multiplied by 1 plus c. So negative 1 equals negative 2 plus c little bit of rearranging so add 2 to both sides that gives us c equals 1. So the equation of the parallel line is y equals negative 2x plus 1. So from this video you should now note that parallel lines always have the same gradient so to find the equation of them we just use the y equals mx plus c equation and we already know the gradient as it's the same for parallel lines so that means we just have to substitute in a set of coordinates to find the y intercept. See that wasn't too difficult was it? Watch our video on perpendicular lines to see how they are slightly different. We still follow the exact same process.