Write an appropriate direct variation equation if y = 30 when x = -10.

Question

I'm going into 12th garde, but I've been playing catch up since 7th. I really need help

Answer 1

Direct variation means one variable is a constant multiple of the other.  The formula for direct variation is y = kx, where k is the constant of variation. If you are studying direct variation, this is what your teacher expects to see, as k is also involved in other form of variation that you will study later.

 

The first step is to solve for k using the information we know. The given point is (-10,30). So...

 

30 = k * -10

 

k = -3

 

Therefore, your equation is now y = -3x.

 

 

 

 

 

Answer 2

The basic equation for a straight line is:

 

y = mx + b

 

Where m is the slope of the line and b is the y-intercept.  The term "direct variation" means that the y-intercept is zero (b = 0); that is, the line crosses through the origin (0,0), so that the equation is:

 

y = mx

 

So all we need to do is find the slope.  The formula for the slope is the change in y over the change in x between any two points, (x₁,y₁) and (x₂,y₂), on the line:

 

m = (y₂-y₁) / (x₂-x₁)

 

So to find m we need two points on the line.  The problem gives us one (-10,30).  Because this line is a "direct variation", we have the second point, (0,0).

 

m = (30-0) / (-10-0) = -30/10 = -3

 

Hence the equation of the line is:

 

y = -3x