write an equation of the line contatining the given point and perpendicular to the line (0,2); 3x+8y=9

Question

write an equation of the line contatining the given point and perpendicular to the line (0,2); 3x+8y=9

Answer 1

So first, you need to find the slope of the given line: 3x+8y=9.  The simplest way is to rewrite in slope-intercept form (y=mx+b).  So we can subtract 3x from both sides and get 8y=-3x+9.  Then divide both sides by 8 so we get: y=-3/8(x)+9/8. The slope of the given line is -3/8.

 

Perpendicular lines have slopes that are negative reciprocals of each other.  The negative of -3/8 is positive 3/8 then we flip for the reciprocal 8/3.

 

We know m=8/3 for the new line but all we are given is a point (0,2).  Hence we need to use point-slope form y-y₁=m(x-x₁) where y₁=2 and x₁=0.

 

Hope this helps!