What is an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x-5y=35?

Answer 1

Hi Leo. The first thing to do is to set up the equation to y=?

So with 4x-5y=35, we can divide everything by -5 to get y=?

Doing that, we have -4/5x+y=-7. Let’s move -4/5x to the right.

Now we have y= 4/5x-7. Now substitute -6 for x and -5 for y.

Starting with y=mx+b, we get -6=4/5(-5)+b

Then we get -6=-4+b, so b=-2.

That makes the answer y=4/5x-2.

Answer 2

First we start with creating an equation for a line parallel to your given equation. To do this we must find the slope of the original equation, because a line parallel to that would have the same slope. Let's first put the original equation into y = form to find the slope.

We first subtract 4x from both sides, leaving: -5y = 35 - 4x

Then, divide both sides by -5, in doing so you can divide 35 and -4x by -5 individually, leaving: y = -7 + (4/5)x

Since the number 4/5 is the coefficient of x with the equation in y = form, 4/5 is our slope.

So an equation parallel to the original equation would be y = (4/5)x

But since we need this equation to pass through the point (-5, -6), we need to substitute those numbers into our new equation. This leaves: -6 = (4/5) x (-5)

This equation is not true however because that would leave -6 = -4

So to make the equation true, we need to add -2, or subtract 2 from our original equation of y = (4/5)x

So our final answer would be: y = (4/5)x - 2