Which line running through (3,4) is perpendicular to y=-3x+4?

Answer 1

The slope of

y

=

−

3

x

4

y=−3x+4 is -3.

The negative reciprocal of -3 is

1

/

3

1/3.

Therefore, a line perpendicular to

y

=

−

3

x

4

y=−3x+4 and passing through (3, 4) would have a slope of

1

/

3

1/3 and can be expressed in the form

y

=

m

x

b

y=mx+b where

m

=

1

/

3

m=1/3 and

(

3

,

4

)

(3,4) satisfies the equation. To find the equation, substitute

m

=

1

/

3

m=1/3 and the point

(

3

,

4

)

(3,4) into the point-slope form:

y

−

y

1

=

m

(

x

−

x

1

)

y−y

1

​

=m(x−x

1

​

),

y

−

4

=

(

1

/

3

)

(

x

−

3

)

y−4=(1/3)(x−3),

y

−

4

=

(

1

/

3

)

x

−

1

y−4=(1/3)x−1,

y

=

(

1

/

3

)

x

3

y=(1/3)x+3.

Therefore, the line perpendicular to

y

=

−

3

x

4

y=−3x+4 and passing through (3, 4) is

y

=

(

1

/

3

)

x

3

y=(1/3)x+3