Math CentralQuandaries & Queries


Question from Hailey, a student:

In the xy-plane,
the line with equation 2x + y = 3
is perpendicular to the line with equation y = mx + b,
where m and b are constants.
What is the value of m?


If you have the equation of a line written in the form y = mx + b then m is the slope of the line. For example the line y = 3/4 x + 6 has slope 3/4. Thus if you put you line 2x + y = 3 in the form y = mx + b you will be able to determine its slope.

If two lines are perpendicular and one has slope m then the other has slope -1/m. Thus a line perpendicular to my line y = 3/4 x + 6 must have slope -1/(3/4) = -4/3. Hence if the line y = mx + b is perpendicular to y = 3/4 x + 6 then m = -4/3.

I hope this helps,

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