Which line is perpendicular to 3x +2y=6? Show all work. Explain using slow relationship.

Answer 1

This is a tricky question! We must start by solving the function for y or writing the equation in y=mx+b form.

3x + 2y = 6

*subtract 3x from both sides of the equal sign*

2y = 6 - 3x

*divide both sides of the equal sign by 2*

y = 3 - 3x/2

To write this equation in y=mx+b form, we simply need to move around the two terms on the right side of the equal sign. The equation should read:

y = -3x/2 + 3

In the above equation, we know that the slope of the line is -3/2 and the y-intercept is 3.

Perpendicular slopes are opposite and reciprocal to the original slope. To find the opposite reciprocal of our slope, we flip the numerator and denominator and divide it by -1. The perpendicular slope should look like this:

-3/2 -> -2/3 -> 2/3

So the new value for m, or the slope of the perpendicular line will be 2/3.

Any function with a slope of 2/3 will be perpendicular to the line 3x + 2y = 6. Here's some examples of lines that would fit this criteria:

y = 2x/3

y = 2x/3 +3

y = 2x/3 -15

etc.

Answer 2

3x + 2y = 6

3x + 2y - 6 = 0

3x - 6 = -2y

(-3/2)x + 3 = y

the slope of the perpendicular must be (2/3)

so the equation of the perpendicular line is:

y = (2/3)x + B

That is the best we can do for now unless you

can provide a point through which the

perpendicular must pass..