Question

What is the slope of a line that is perpendicular to a line whose equation 3y=-4x+2

Answer 1

For this case we have to by definition, if two lines are perpendicular then the product of its slopes is -1. That is to say:

$m_ {1} * m_ {2} = - 1$

We have the following equation:

$3y = -4x + 2\\y = - \frac {4} {3} x + \frac {2} {3}$

Thus, the equation is of the pending-intersection form$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have to:

$m_ {1} = - \frac {4} {3}$

Thus, we find $m_ {2}$:

$m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- \frac {4} {3}}\\m_ {2} = \frac {3} {4}$

Thus, the slope of the line perpendicular to the given line is:

$m_ {2} = \frac {3} {4}$

ANswer:

$m_ {2} = \frac {3} {4}$