Question

write an equation of the line that passes through (3, 8 )and is perpendicular to the line Y =5x-4

Answer 1

Recalll that the general equation fo the line is of the form y=mx+b where m is the slope and b is the y intercept. Also, remember that if we have two lines y=m1x+b1 and y=m2x+b2, they are perpendicular if and only if m1*m2=-1.

Let's construct the equation of the line we want. Say y=mx+b. So we must find the value of m and b. We are given the line y=5x-4. The slope of this line is 5. Since we want them to be perpendicular, it must happen that

$m\cdot5=-1$

if we divide by 5 on both sides, we get

$m=\frac{-1}{5}$

this means that the equation we want, so far, is

$y=\frac{-1}{5}x+b$

Now, since this line passes through the point (3,8) it must happen that whenever we replace x by 3, y should be replaced by 8. Then we have the equation

$8=-\frac{1}{5}\cdot3+b$

Then, if we add 3/5 on both sides, we get

$b=8+\frac{3}{5}=\frac{43}{5}$

So, the equation of our perpendicular line is

$y=-\frac{1}{5}\cdot x+\frac{43}{5}$