#9 can anyone solve this for will give !

y

=

−

1

6

x

Explanation:

General Introduction

Given:

y

=

6

x

Compare to the standard equation form of  

y

=

m

x

+

c

Where  

m

is the gradient (slope)

Looking at the question we see that the gradient is 6.

This means that for 1 along on the x-axis the line has gone up 6 on the y-axis.

y

=

6

x

→

gradient  

→

m

=

6

'

.

Building the equation of the perpendicular line

A line perpendicular to  

y

=

m

x

+

c

has gradient  

−

1

m

If  

m

=

6

then  

−

1

m

=

−

1

6

So the straight line perpendicular to that given has the equation

y

=

−

1

m

x

+

c

→

y

=

−

1

6

x

+

c

'

.

Determine the value of the constant  

c

This line passes through the point  

(

x

,

y

)

→

(

6

,

−

1

)

So by substitution

y

=

−

1

6

x

+

c

→

−

1

=

−

1

6

(

6

)

+

c

⇒

c

=

0

so the equation of the perpendicular line is:

y

=

−

1

6

x

Step-by-step explanation: