Question

I’ve tried working it out but I’m still having a lot of trouble with this.

Answer 1

Greetings!

Convert the equation to slope y-intercept form:

`-9y=-18x+28`


`(-9y)/(-9)= (-18x+28)/(-9)`


`y=2x-(28)/(9)`

The Slope of this equation is represented by 2 (or
`(2)/(1)`). In order to create a line perpendicular to this line, they must have negative reciprocals. The formula for this is:
`(m_(1) )( m_(2))=-1` (m represents the slope each line).

Input the values we know:

`(2)( m_(2))=-1`

Solve:

`2m_(2)=-1`


`(2m_(2))/(2)= (-1)/(2)`


`m_(2)= (-1)/(2)`

Arrange the new equation in slope y-intercept form:

`y= (-1)/(2)x+b`

Input a coordinate point into the equation:

`(6)= (-1)/(2)(-11)+b`

Solve

`(6)= (11)/(2)+b`


`(12)/(2)= (11)/(2)+b`


`(12)/(2)-(11)/(2)=b`


`(1)/(2)=b`

The y-intercept is equal to
`(1)/(2)`

Now using the information we have, arrange the equation in slope y-intercept form:

`\left[\begin{array}{ccc}y= (-1)/(2)x+ (1)/(2) \end{array}\right]`

Hope this helps!
-Benjamin