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irina [24]
3 years ago
14

Find the equation of the straight line that has slope m = -6 and passes through point (2, -7)

Mathematics
1 answer:
MAXImum [283]3 years ago
3 0

Answer:

y

=

3

2

x

+

1

Explanation:

To find the slope  

(

m

)

of the straight line that passes through two points  

(

x

1

,

y

1

)

and  

(

x

2

,

y

2

)

apply:

(

y

1

−

y

2

)

=

m

(

x

1

−

x

2

)

In this example our two points are  

(

0

,

1

)

and  

(

2

,

4

)

Hence:  

(

1

−

4

)

=

m

(

0

−

2

)

−

3

=

−

2

m

→

m

=

3

2

The equation of a straight line in slope  

(

m

)

and intercept  

(

c

)

form is:

y

=

m

x

+

c

In this example:

y

=

3

2

x

+

c

Since the point  

(

0

,

1

)

is on this line  

→

1

=

0

+

c

Hence,  

c

=

1

∴

y

=

3

2

x

+

1

is our required straight line.

Step-by-step explanation:

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Daniel has 6 teaspoons of salt. The ratio of teaspoons to tablespoons is 3 :1. How many tablespoons of salt does Daniel have
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8 0
3 years ago
Diego is collecting dimes and nickels in a jar. He has collected $22.25 so far. The relationship between the numbers of dimes an
svet-max [94.6K]

Answer:

Correct options are:

a) ( 0 , 445 )

d) ( 118 , 209 )

e) ( 172 , 101 )

Step-by-step explanation:

A nickel is worth 5 cents $0.05

A dime is worth 10 cents = $0.10

The relationship between the numbers of dimes and nickels, and the amount of money in dollars is represented by the equation 0.10d+0.05n=22.25. Select the THREE values (d,n) that could be solutions to the equation.

a) ( 0 , 445 )

b) ( 0.50 , 435 )

c) ( 233 , 21 )

d)( 118 , 209 )

e)( 172 , 101 )

Verifying the options

a) ( 0 , 445 )

0.10d+0.05n=22.25.

= 0.10(0) + 0.05(445) = 22.25

= 22.25 = 22.25

Options a) is correct

b) ( 0.50 , 435 )

0.10d+0.05n=22.25.

= 0.10(0.50) + 0.05(435) = 22.25

= 21.8 ≠ 22.25

Option b is incorrect

c) ( 233 , 21 )

0.10d+0.05n=22.25.

= 0.10(233) + 0.05(21) = 22.25

= 24.35 ≠22.25

Option c is incorrect

d) ( 118 , 209 )

0.10d+0.05n=22.25.

= 0.10(118) + 0.05(209) = 22.25

= 22.25 = 22.25

Option d) is correct

e) ( 172 , 101 )

0.10d+0.05n=22.25.

= 0.10(172) + 0.05(101) = 22.25

= 22.25 = 22.25

Option e) is correct

5 0
3 years ago
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