+0

# what is the slope of any line perpendicular to the line 4/(3x+2y)=-14?

0
313
2

what is the slope of any line perpendicular to the line 4/(3x+2y)=-14?

Guest Feb 28, 2015

#2
+227
+5

What you want to do first is find the equation of the line. We'll put it into the form y=mx+b, where m is the slope and b is the y-intercept.

$$\frac{4}{3x+2y} = -14$$

Well, we want y all by itself, so what should we do? Let's multiply both sides of the equation by the denominator!

$$\frac{4}{3x+2y} * (3x+2y) = -14 * (3x+2y) \Rightarrow 4 = -42x - 28y$$

I went ahead and used the distributive property to help simplify the problem. Now let's keep making y alone! So, y doesn't like x, so we'll take him away by adding 42x to each side of the equation.

$$4 + 42x = -42x - 28x +42x \Rightarrow 4 + 42x = -28y$$

The y still isn't alone. He has that -28 right next to him! Let's divide both sides by -28 to get rid of him.

$$\frac{4+42x}{-28} = \frac{-28y}{-28} \Rightarrow -\frac{1}{7} - \frac{3}{2}x = y$$

Now y is alone! let's rewrite this as the whole y=mx+b form.

$$y = -\frac{3}{2}x-\frac{1}{7}$$

Remember, m is the slope. So, m=-3/2!

Now, to do the perpendicular of a line, just flip the slope and change the sign! So, the new perpendicular slope equals 2/3!

ThisGuy  Feb 28, 2015
Sort:

#1
+26625
+5

First rewrite this as follows:

Multiply through by 3x + 2y

4 = -14(3x + 2y)

4 = -42x - 28y

Ad 28y to both sides and subtract 4 from both sides

28y = -42x - 4

Divide through by 28

y = -(42/28)x - 4/28  or y = -(3/2)x - 1/7

The slope of this line is -(3/2) so the slope of a line perpendicular to this is +(2/3)

.

Alan  Feb 28, 2015
#2
+227
+5

What you want to do first is find the equation of the line. We'll put it into the form y=mx+b, where m is the slope and b is the y-intercept.

$$\frac{4}{3x+2y} = -14$$

Well, we want y all by itself, so what should we do? Let's multiply both sides of the equation by the denominator!

$$\frac{4}{3x+2y} * (3x+2y) = -14 * (3x+2y) \Rightarrow 4 = -42x - 28y$$

I went ahead and used the distributive property to help simplify the problem. Now let's keep making y alone! So, y doesn't like x, so we'll take him away by adding 42x to each side of the equation.

$$4 + 42x = -42x - 28x +42x \Rightarrow 4 + 42x = -28y$$

The y still isn't alone. He has that -28 right next to him! Let's divide both sides by -28 to get rid of him.

$$\frac{4+42x}{-28} = \frac{-28y}{-28} \Rightarrow -\frac{1}{7} - \frac{3}{2}x = y$$

Now y is alone! let's rewrite this as the whole y=mx+b form.

$$y = -\frac{3}{2}x-\frac{1}{7}$$

Remember, m is the slope. So, m=-3/2!

Now, to do the perpendicular of a line, just flip the slope and change the sign! So, the new perpendicular slope equals 2/3!

ThisGuy  Feb 28, 2015

### 13 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details