How Do You Write an Equation for Direct Variation Given a Point?

y=kx is the general equation for direct variation
k is the constant of variation
We can plug 4 in for y and 2 in for x in the direct variation equation
Then we can just solve for k
When we plug 2 in for k in the direct variation equation, we get an equation that relates our x's and y's
To find y when x is 4, we can just plug 4 in for the x of our new equation of y=2x
y=2•4=8

1. The equation for direct variation is y=kx
2. We can just plug 4 in for y and 2 in for x to find the value of k
1. The equation for direct variation is y=kx
2. We can just plug 4 in for y and 2 in for x to find the value of k
3. k is the constant of variation
1. The equation for direct variation is y=kx
2. We can just plug 4 in for y and 2 in for x to find the value of k
3. k is the constant of variation
1. The equation for direct variation is y=kx
2. So we get 4=k•2
1. We can just plug 4 in for y and 2 in for x to find the value of k
2. Divide both sides of "4=k•2" by 2 to get k=2
3. The equation for direct variation is y=kx
4. k is the constant of variation
1. Since we now know k, we can rewrite the general equation for direct variation to reflect the values we were given, x=2 and y=4
1. We can just plug 2 in for k of the direct variation equation (y=kx) to find our equation
1. Here we plugged 2 in for k into y=kx
1. We can just plug 4 in for x of our new equation to find y
2. Our new equation is y=2x
1. We can just plug 4 in for x of our new equation to find y
2. Our new equation is y=2x
1. The equation we're plugging into is y=2x
1. We just plugged 4 in for x in y=2x
1. y=2•4=8
2. y=8 when x=4 because our direct variation equation is y=2x

Suppose that y varies directly with x. Write a direct variation equation that relates x and y if y = 4 when x = 2. Then find y when x = 4.