   SEARCH HOME Math Central Quandaries & Queries  Question from Jesse, a student: How do you write an equation of a line that is perpendicular to y+2x+3 and passes through (3,4); I don't understand the steps of how to do this???? Hi Jesse.

I presume you meant to write y = 2x + 3.

If the equation of a line is written in the form

y = mx + b

then m is the slope so the first line has a slope of 2.

Parallel lines have the same slope and perpendicular lines have negative reciprocal slopes. That is, if
y = mx + b and y = kx + c are perpendicular then k = -1/m. Thus a line which is perpendicular to your line has a slope of -1/m = -1/2.

Hence a line perpendicular to your first line has an equation of the form

y = -1/2 x + b for some number b.

Since you know that this line passes through the point (3,4), you know that when x = 3 then y = 4. So you can put these values into the last equation to find the value of b.

4 = -1/2 (3) + b

Solve for b and you have all the pieces you need to write the equation of the perpendicular line.

Stephen and Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.