Question

What is an equation of the line that passes through the point (5,8) and is parallel to the line 4x−5y=45?

Answer 1

4x-5y=45
4x-45=5y

(4/5)x+9=y

A line parallel to this one would have the same gradient (since the lines won't get closer or go farther) and maybe a different y intercept ("maybe" because a line would be parallel to itself)

So'
y= (4/5)x + c

Line passes through (5,8)
Plug in the x and y values into the equation to find c:
(4/5)(5) + c =8
4+c=8
Therefore, c = 8-4 = 4

So the new equation is y= (4/5)x+4

Now, we could put this back into the same format as the question because why not.
We find the common denominator of the right hand side of the equation:
y= (4/5)x +(20/5) = (4x+20)/5
Multiply both sides of the equation by 5:
5y = 4x+20
Therefore 4x-5y = -20.