which equation has as its graph a line perpendicular to a line that has a slope of 2 over 3

Question

find the perpendicular line of the slope 2 over 3 

Answer 1

Dear Mohammed,

 

In general, when working with linear equations of the type

 

y = mx + b     Equation 1.

 

the line perpendicular to Equation 1 will have a slope of (-1/m)

 

So, if you have a line with a slope of (2/3), any line perpendicular will have a slope of (-3/2).

 

I hope this helps.

Answer 2

The equation you gave is represented as y=(2/3)x

 

When working with parallel and perpendicular lines the thing you're dealing with is the slope. To have a line be PARALLEL, meaning the two lines with never intersect, means the lines have to have the SAME SLOPE.

 

When working with perpendicular lines, however, we want the lines to intersect at a 90 degree angle. To do this we need to use the OPPOSITE RECIPROCAL of the slope we're starting with.

SO- Opposite: changing the sign of the original slope to the "negative" of what it is.
       We started with a POSITIVE 2/3, so our NEW slope will be NEGATIVE ?/?

SO- Reciprocal: flipping the fraction so the denominator now becomes the numerator and vice verse.

       We started with 2/3, so our NEW fraction will be 3/2

Now we need to make sure we have the OPPOSITE RECIPROCAL
   Starting with 2/3 we now get -3/2 as the slope for a line perpendicular to a line with original slope of 2/3.