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

 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:

step-by-step explanation:

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