Question

What is an equation of the line that passes through the point (-4,-6)(−4,−6) and is perpendicular to the line 4x+5y=25?

Answer 1

y=(5/4)x-1

First you put the equation into y=mx+b form:
1. move the 4x to the other side
5y=-4x+25
2. divide by 5 on both sides
y=(-4/5)x+5

Next, since the line has to be perpendicular, you take the negative reciprocal of the slope (flip the fraction and put the opposite sign)
1. 5/4

Now, find the y intercept (the b)
1. set up the equation
-6=(5/4)(-4)+b
2. multiply the 5/4 and -4
-6=-5+b
3. move the -5 to the other side (add it)
-1=b

Now, put all the elements together
1. y=(5/4)x-1