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3 years ago

Use slopes and y-intercepts to determine if the lines 6x+y=−1 and −2x−5y=1 are parallel.

Mathematics

1 answer:

kobusy [5.1K]3 years ago

7 0

Answer:

The two lines are not parallel.

Step-by-step explanation:

Every linear equation follows this structure:

y = mx + b

y is the y value

x is the x value

m is the gradient/slope of the line

b (or sometimes c) is the y-intercept of the line

Firstly, we have to get the y term on one side by itself.

6x + y = -1

-6x -6x

y = -6x - 1

-2x -5y = 1

+2x +2x

-5y = 2x + 1

Secondly, we make it so the y term is just the y value.

The first equation is already like this, so we don't need to do anything to that.

-5y = 2x + 1

÷ -5 ÷ -5

y = (2x + 1) / -5

This can be expanded and simplified to:

y = -2/5x - 1/5

Thirdly, we have to compare the slopes and y-intercepts.

y = -6x - 1

y = 2/5x - 1/5

If the slopes are the same and the y-intercepts are different, they are parallel. However, the slopes are different, therefore they are not parallel.

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Arada [10]

Answer:

65.56°

Step-by-step explanation:

We know that if we take dot product of two vectors then it is equal to the product of magnitudes of the vectors and cosine of the angle between them

That is let p and q be any two vectors and A be the angle between them

So, p·q=|p|*|q|*cosA

⇒ $cosA=\frac{u.v}{|u||v|}$

Given u=-8i-3j and v=-8i+8j

$|u|=\sqrt{(-8)^{2}+ (-3)^{2}} =8.544$

$|v|=\sqrt{(-8)^{2}+ (8)^{2}} =11.3137$

let A be angle before u and v

therefore, $cosA=\frac{u.v}{|u||v|}=\frac{(-8)*(-8)+(-3)*(8)}{8.544*11.3137} =\frac{40}{96.664}$

⇒ $A=arccos(\frac{40}{96.664} )=arccos(0.4138 )=65.56$

Therefore angle between u and v is 65.56°

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The answer is in the picture
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