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:

b. f(x) = –√x + 3this is the correct answer

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus