Identify the equation of a line perpendicular to y=3/5x-6 and passing through (1,4)
in slope-intercept form

The equation of perpendicular line is  

y

=

−

5

3

x

+

17

3

.

Explanation:

The slope of the line  

y

=

3

5

x

−

6

is  

m

1

=

3

5

[obtained by

comparing standard slope-intercept form of line with slope

m

;

y

=

m

x

+

c

] . We know the product of slopes of two

perpendicular lines is  

−

1

, i.e  

m

1

⋅

m

2

=

−

1

or

3

5

⋅

m

2

=

−

1

or  

m

2

=

−

5

3

. Let the equation of perpendicular line in

slope - intercept form is  

y

=

m

x

+

c

;

m

=

m

2

=

−

5

3

∴

y

=

−

5

3

x

+

c

. The line passes through point  

(

1

,

4

)

, which

will satisfy the equation of line  

∴

4

=

−

5

3

⋅

1

+

c

∴

c

=

4

+

5

3

or  

c

=

17

3

Hence the equation of perpendicular line is

y

=

−

5

3

x

+

17

3

-2/3

Step-by-step explanation: