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# Writing equations of perpendicular lines (example 2)

## Video transcript

find the equation of a line perpendicular to this line that passes through the point 2 comma 8 so this first piece of information that it's perpendicular to that line right over there what does that tell us well if it's perpendicular to this line its slope has to be the negative inverse of 2/5 so it's slope the negative inverse of 2/5 the inverse of 2/5 is 5 let me do it in a better color a nicer green if this lines slope is negative 2/5 the equation of the line we have to figure out that's perpendicular it's slope is going to be the inverse so instead of 2/5 it's going to be five halves instead of being a negative it's going to be a positive so this is the negative inverse of negative 2/5 right you take the negative sign it becomes positive you swap the 5 and the 2 you get 5 halves so that is going to have to be our slope and we can actually use the point-slope form right here it goes through this point right there so let's use point-slope form Y minus this Y value which has to be on the line is equal to our slope five halves times X minus this x value the x-value when y is equal to 8 and this is the equation of the line in point-slope form if you want to put it in slope-intercept form you can just do a little bit of algebra algebraic manipulation y minus 8 is equal to let's distribute the five halves oh five halves X minus 5 halves times two is just five and then add 8 to both sides you get Y is equal to five halves x add 8 to negative 5 so plus three and we are done