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Tresset [83]
3 years ago
10

What is the equation of the line that passes through the pont (6,2) and has a of -2/3

Mathematics
1 answer:
ss7ja [257]3 years ago
8 0

Answer:  y

=

−

2

3

x

+

2

Explanation:

Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.

Point-Slope Formula:  

y

−

y

1

=

m

(

x

−

x

1

)

, where  

m

is the slope of the line and  

x

1

and  

y

1

are x and y coordinates of a given point.

We can summarize the information already given:

m

=

−

2

3

x

1

=

6

y

1

=

−

2

Using this information, we can substitute these values onto the point-slope formula:

y

−

(

−

2

)

=

−

2

3

(

x

−

(

6

)

)

y

+

2

=

−

2

3

(

x

−

6

)

The equation above is the equation of the line in point-slope form. If we wanted to have the equation in  

y

=

m

x

+

b

form then we simply solve the equation above for  

y

y

+

2

=

−

2

3

x

+

12

3

y

+

2

−

2

=

−

2

3

x

+

12

3

−

2

y

=

−

2

3

x

+

12

3

−

2

(

3

3

)

y

=

−

2

3

x

+

12

3

−

6

3

y

=

−

2

3

x

+

6

3

y

=

−

2

3

x

+

2y

=

−

2

3

x

+

2

Explanation:

Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.

Point-Slope Formula:  

y

−

y

1

=

m

(

x

−

x

1

)

, where  

m

is the slope of the line and  

x

1

and  

y

1

are x and y coordinates of a given point.

We can summarize the information already given:

m

=

−

2

3

x

1

=

6

y

1

=

−

2

Using this information, we can substitute these values onto the point-slope formula:

y

−

(

−

2

)

=

−

2

3

(

x

−

(

6

)

)

y

+

2

=

−

2

3

(

x

−

6

)

The equation above is the equation of the line in point-slope form. If we wanted to have the equation in  

y

=

m

x

+

b

form then we simply solve the equation above for  

y

y

+

2

=

−

2

3

x

+

12

3

y

+

2

−

2

=

−

2

3

x

+

12

3

−

2

y

=

−

2

3

x

+

12

3

−

2

(

3

3

)

y

=

−

2

3

x

+

12

3

−

6

3

y

=

−

2

3

x

+

6

3

y

=

−

2

3

x

+

2

Step-by-step explanation:

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olga_2 [115]

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Step-by-step explanation:

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6 0
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A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeles
MA_775_DIABLO [31]

Answer:

[0.184, 0.266]

Step-by-step explanation:

Given:

Number of survey n =280

Number of veterans = 63

Confidence interval = 90%

Computation:

Probability of veterans = 63/280

Probability of veterans =0.225

a=0.1

Z(0.05) = 1.645 (from distribution table)

Confidence interval = 90%

So,

p ± Z*√[p(1-p)/n]

0.225 ± 1.645√(0.225(1-0.225)/280)

[0.184, 0.266]

4 0
3 years ago
HI PLZ HELPI NEED AN ANSWER!! (And will mark brainliest if a legit answer thanks)
trapecia [35]

Option 3: a 90 degree rotation clockwise

You can tell that it is 90 degrees because the original started completely in quadrant 2 and the final image is completely in quadrant 1. If it was only rotated 45 degrees the final image would be part in quadrant 2 and part in quadrant 1. It was rotated clockwise because that is the way a clock goes.

Hope this helps! ;)

6 0
3 years ago
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