Question

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

Answer 1

we know that

if two lines are perpendicular, then the product of their slopes is equal to minus one

so

$m1*m2=-1$

Step 1

Find the slope of the given line

we have

$3y=-4x+2$

Solve for y

Divide by $3$ both sides

$3y/3=(-4x+2)/3$

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

the slope of the given line is $m1=-\frac{4}{3}$

Step 2

Find the slope  of a line that is perpendicular to the given line

we have

$m1=-\frac{4}{3}$

$m1*m2=-1$

$m2=-1/m1$

substitute the value of m1

$m2=-1/(-4/3)=\frac{3}{4}$

therefore

the answer is

the slope is $\frac{3}{4}$