Through (3, 4) and perpendicular to y = (1/3)x - 3

3

x

−

2

y

=

7

Explanation:

Write the standard form of the line that goes through  

(

3

,

1

)

and is perpendicular to  

y

=

−

2

3

x

+

4

.

The equation  

y

=

−

2

3

x

+

4

is in slope intercept form

y

=

m

x

+

b

where  

m

= slope and  

b

= the  

y

intercept.

The slope of this line is then  

m

=

−

2

3

A perpendicular slope is the opposite sign reciprocal. So, we change the sign of  

−

2

3

and switch the numerator and denominator.

Perpendicular slope  

m

=

3

2

To find the equation of the new line, use the point slope equation

y

−

y

1

=

m

(

x

−

x

1

)

where  

m

=

slope and  

(

x

1

,

y

1

)

is a point.

The slope is  

3

2

and the point is the given point  

(

3

,

1

)

.

y

−

1

=

3

2

(

x

−

3

)

a

a

a

Distribute

y

−

1

=

3

2

x

−

9

2

Standard form is  

a

x

+

b

y

=

c

where  

a

,

b

and

c

are integers and  

a

is positive.

a

a

2

(

y

−

1

=

3

2

x

−

9

2

)

a

a

a

Multiply the equation by  

2

a

a

a

a

a

2

y

−

2

=

3

x

−

9

−

3

x

a

a

a

a

a

a

a

−

3

x

a

a

a

Subtract  

3

x

from both sides

−

3

x

+

2

y

−

2

=

−

9

a

a

a

a

a

a

a

a

+

2

a

a

a

+

2

a

a

a  Add  2  to both sides  − 3 x + 2 y = − 7 − 1 ( − 3 x + 2 y = − 7 ) a a a Multiply the equation by  − 1 3 x − 2 y = 7

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.

nlgqer

step-by-step