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navik [9.2K]
3 years ago
13

What is the equation of a line that has a slope of 3 and a y-intercept of -3

Mathematics
2 answers:
LenKa [72]3 years ago
7 0

Answer:

y = 3x-3

Step-by-step explanation:

y = mx+b

m is your slope and b is your y-intercept

plug those numbers in

y = 3x-3

LUCKY_DIMON [66]3 years ago
6 0

The slope-intercept form:

y = mx + b

m - slope

b - y-intercept

We have m = 3 and b = -3. Substitute:

<h3>y = 3x - 3</h3>
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Is anybody else here to help me ??​
Akimi4 [234]

Answer:

\cot(x)+\cot(\frac{\pi}{2}-x)

\cot(x)+\tan(x)

\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}

\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})

\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})

\csc(x)[\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}]

\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}]

\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}]

\csc(x)[\frac{1}{\cos(x)}]

\csc(x)[\sec(x)]

\csc(x)[\csc(\frac{\pi}{2}-x)]

\csc(x)\csc(\frac{\pi}{2}-x)

Step-by-step explanation:

I'm going to use x instead of \theta because it is less characters for me to type.

I'm going to start with the left hand side and see if I can turn it into the right hand side.

\cot(x)+\cot(\frac{\pi}{2}-x)

I'm going to use a cofunction identity for the 2nd term.

This is the identity: \tan(x)=\cot(\frac{\pi}{2}-x) I'm going to use there.

\cot(x)+\tan(x)

I'm going to rewrite this in terms of \sin(x) and \cos(x) because I prefer to work in those terms. My objective here is to some how write this sum as a product.

I'm going to first use these quotient identities: \frac{\cos(x)}{\sin(x)}=\cot(x) and \frac{\sin(x)}{\cos(x)}=\tan(x)

So we have:

\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}

I'm going to factor out \frac{1}{\sin(x)} because if I do that I will have the \csc(x) factor I see on the right by the reciprocal identity:

\csc(x)=\frac{1}{\sin(x)}

\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})

\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})

Now I need to somehow show right right factor of this is equal to the right factor of the right hand side.

That is, I need to show \cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)} is equal to \csc(\frac{\pi}{2}-x).

So since I want one term I'm going to write as a single fraction first:

\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)}

Find a common denominator which is \cos(x):

\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}

\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}

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By  the Pythagorean Identity \cos^2(x)+\sin^2(x)=1 I can rewrite the top as 1:

\frac{1}{\cos(x)}

By the quotient identity \sec(x)=\frac{1}{\cos(x)}, I can rewrite this as:

\sec(x)

By the cofunction identity \sec(x)=\csc(x)=(\frac{\pi}{2}-x), we have the second factor of the right hand side:

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Let's just do it all together without all the words now:

\cot(x)+\cot(\frac{\pi}{2}-x)

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\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}]

\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}]

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\csc(x)[\sec(x)]

\csc(x)[\csc(\frac{\pi}{2}-x)]

\csc(x)\csc(\frac{\pi}{2}-x)

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Which of the following is a quadratic equation?
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Answer:

  3)  4x² -1

Step-by-step explanation:

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1) an exponential equation (the variable is in the exponent)

2) a cubic equation (degree = 3)

3) a quadratic equation

4) a linear equation (degree = 1)

4 0
1 year ago
Girls to boys 5 to 8. How many girls are in the class if there are 24 boys
ValentinkaMS [17]

Answer:

Step-by-step explanation:

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3 years ago
Read 2 more answers
Drag each label to the correct location on the image.
dolphi86 [110]

Answer:

The answer will be listed below.

Step-by-step explanation:

No Solution: -2z+2+4z=16/5+2z-6/5; 5r+2=6r+3-r

One Solution: 3/2x+2.3-1/2x=4.3+x; 2x+2/3=2x+4/5-4x; 32p-2.5+2.1p=5p-7/2

Infinite Solution: 17/4+4.2y-9/4=2.2y+6+2y-4

Note: Remember that infinite solution is like 1=1 or 5x+2=5x+2. No solution is where it's like 0=1. 1 solution is where it's like x=2.

4 0
3 years ago
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! SUPER IMPORTANT QUESTION!!!
Anettt [7]

Answer:

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Step-by-step explanation:

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We assumed, the diameter of earth is 7917.5 miles.

So, the radius = \frac{7917.5}{2} = 3958.75 miles

So, using the cosine formula, we have,

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i.e. a^{2}=31343403.13\times 0.0012

i.e. a^{2}=37612.08

i.e. a= 193.94 miles.

Hence, the distance between two cities is 193.94 miles.

8 0
2 years ago
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