1 Answer

Rafak · Answer 1 · 2023-09-09T18:38:33+0000

Solution:

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

solving for 3y, this equation is equivalent to:

that is:

now, solving for y, we obtain:

that is:

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

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:

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

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

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