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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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<span>x^2 + 15x + 56.25 = 105.25

    "Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
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   Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?" Well, we know that the left hand side of the equation can now be written as
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