1. Tell whether x and y show direct variation.
a. 5x - 3y = 0
b. x = y - 2 / 9
2. The variables x and y vary directly. Use the values to find the constant of proportionality and write an equation that relates x and y.
a. y = 4; x = 6
b. y = 2; x = 10
To determine if two variables, x and y, show direct variation, we need to check if they satisfy the equation y = kx, where k is the constant of proportionality.
1a. 5x - 3y = 0
Rearranging the equation, we get:
3y = 5x
Dividing both sides by 3, we have:
y = (5/3)x
Since y is proportional to x (with a constant of proportionality 5/3), x and y show direct variation.
1b. x = (y - 2) / 9
Rearranging the equation, we get:
x = (1/9)y - 2/9
The equation is not in the form of y = kx. Therefore, x and y do not show direct variation.
2a. Given: y = 4, x = 6
Using the formula y = kx, we can substitute the given values to solve for k:
4 = k * 6
Dividing both sides by 6, we get:
k = 4/6 = 2/3
The constant of proportionality is 2/3. Therefore, the equation relating x and y is y = (2/3) x.
2b. Given: y = 2, x = 10
Using the formula y = kx, we can substitute the given values to solve for k:
2 = k * 10
Dividing both sides by 10, we get:
k = 2/10 = 1/5
The constant of proportionality is 1/5. Therefore, the equation relating x and y is y = (1/5)x.