Question

What is an equation of the line that passes through the point (8, -8) and isperpendicular to the line 4x - 3y = 18?

Answer 1

Let us denote by L1 the line given by the following equation:

`4x-3y=18`

solving for 3y, this equation is equivalent to:

`4x-18=3y`

that is:

`3y=4x-18`

now, solving for y, we obtain:

`y=(4)/(3)x-(18)/(3)=(4)/(3)x-6`

that is:

`y=(4)/(3)x-6`

now, perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is

`m=-(3)/(4)`

with this information, we can say that the provisional slope-intercept form of the perpendicular line to L1 is:

`y\text{ =-}(3)/(4)x+b`

our goal is now to find the y-intercept b of this line. To do this, we can replace the point (x,y)=(8, -8) into the previous equation, to get:

`-8\text{ =-}(3)/(4)(8)+b`

solving for b, we get:

`b=-8+(3)/(4)(8)=-2`

so that, we can conclude that the equation of the line would be:

`y\text{ =-}(3)/(4)x-2`