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

h= 12 inches

step-by-step explanation: