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 $\frac{3}{4}$

Answer 2

The slope of a line that is perpendicular to a line of the given equation is $\frac{3}{4}$

Given the following equation;

• $3y =-4x +2$

To find the slope of a line that is perpendicular to a line of the given equation:

In Mathematics, the slopes of two lines are said to be perpendicular when the product of these slopes is equal to negative one (-1).

Mathematically, this is given by:

$m_1 \times m_2 = -1$   ...equation 1.

First of all, we would determine the slope of the given equation:

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

Slope, $m_1$ = $\frac{-4}{3}$

Substituting slope 1 into eqn 1, we have:

$\frac{-4}{3} \times m_2 = -1\\\\-4m_2 = -3\\\\m_2 = \frac{3}{4}$

Read more: https://brainly.com/question/14096662