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mx + 3y = 7 and 2x - 3y = 5 are perpendiculars. What should be the value of m? 

Sagot :

First step: express the equation into the form y = (slope)x + b; y is alone on one side

2x-3y = 5 <----- subract 2x to both sides
-3y = -2x + 5; divide both sides by -3
y = (-2/3)x - 5/3 <--- this is the first equation

mx + 3y = 7 <---- subtract mx to both sides
3y = -mx + 3 <----- divide both sides by 3
y = (-m/3)x + 1 <---- this is the second equation
Now determine the slope of equations 1 and 2.
[the slope is anything that is multiplied to x]
Equation 1: -2/3 <---slope1
Equation 2: -m/3 <----slope2
Now if two line are perpendicular then the slopes of the two equations are negative reciprocals.
Example, if the slope of line1 is 3/5 then the slope of line2 that will make it parallel to line1 is -5/3 <---- notice that you flip the top and bottom numbers and multiplies it to negative 1

Second step get the negative reciprocal of one the slopes and equate it to the slope of the other: -RECIPROCAL  slope 1 = slope2
the negative reciprocal of -2/3 is 3/2
then equate it to -m/3
3/2 = -m/3 <---- multiply both sides by 3
9/2 = -m <------ multiply by -1
-9/2 = m <----- flip the equation
m = -9/2 <---- this is the value of m

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