Question

Find the direct variation equation of the graph through the points (0, 0) and (1, -2).

Answer 1

A direct variation equation would relate two variables to one another through the use of various operations. So, assuming that this function is a line, we can see that our direct variation equation would take the form y=mx+b. where b is a constant representing the y intercept, m is the slope (relating your variables), and x and y are your two variables.

We can start by graphing these two points on a catesian coordinate system.

Through observation we can see that our y intercept (the point where the line between the two points intersects the y-axis) is zero. so b=0.

now, to find our m, which will serve as the constant relating the x and y variables, we can just use a simple equation \[(y _{2}-y _{2})/(x _{2}-x _{1})\]
which tells us the change in the y variable with respect to the change in x variable.
In simple terms, it tells us the value of y when x is a certain number.

So, for this problem we would have
\[(y _{2}-y _{2})/(x _{2}-x _{1})\]
\[(0-(-2))/(0-1)\]
\[=(2/-1)\]
\[=-2\]
which is the value of our m (a.k.a. the slope)

now we use the general direct variation equation y=mx+b to represent our equation, substituting uor values of m and b (which serve to relate our two variables x and y)

m=-2 and b=0 so,
y=-2x+0
y=-2x is the direct variation equation for the graph of the function