Question

Pleeeeese help me as fast as you can!!!

Answer 1

A.
`y=3x-10`

C.
`y+6=3(x-15)`

Explanation:

Given:

The given line is
`6x+18y=5`

Express this in slope-intercept form
`y=mx+b`, where m is the slope and b is the y-intercept.

`6x+18y=5\\18y=-6x+5\\y=-(6)/(18)x+(5)/(18)\\y=-(1)/(3)x+(5)/(18)`

Therefore, the slope of the line is
`m=-(1)/(3)`.

Now, for perpendicular lines, the product of their slopes is equal to -1.

Let us find the slopes of each lines.

Option A:

`y=3x-10`

On comparing with the slope-intercept form, we get slope as
`m_(A)=3`.

Now,
`m* m_(A)=-(1)/(3)* 3=-1`. So, option A is perpendicular to the given line.

Option B:

For lines of the form
`x=a`, where, a is a constant, the slope is undefined. So, option B is incorrect.

Option C:

On comparing with the slope-point form, we get slope as
`m_(C)=3`.

Now,
`m* m_(C)=-(1)/(3)* 3=-1`. So, option C is perpendicular to the given line.

Option D:

`3x+9y=8\\9y=-3x+8\\y=-(3)/(9)x+(8)/(9)\\y=-(1)/(3)x+(8)/(9)`

On comparing with the slope-intercept form, we get slope as
`m_(D)=-(1)/(3)`.

Now,
`m* m_(D)=-(1)/(3)* -(1)/(3)=(1)/(9)`. So, option D is not perpendicular to the given line.