B. The variables x and y vary directly. Use the values to find the constant of proportionality and write and equation that relates x and y.
1. y - 4; x = 6
2. y = 2; x = 10
x goes from 6 to 10, y goes from -4 to 2
so x changed by 4, y changed by 6
y=mx+b
y=6/4 * x + b now test the first point
-4=6/4 * 6+b
b=-4 -9=-13
y=1.5 x -13
To find the constant of proportionality in a direct variation problem, we can use the formula:
k = y / x
where k represents the constant of proportionality.
1. For the first set of values, y = 4 and x = 6. Plugging these values into the formula, we get:
k = 4 / 6 = 2/3
So the constant of proportionality is 2/3.
To write the equation that relates x and y, we can now substitute the constant of proportionality into the equation in the form y = kx:
y = (2/3) * x
Thus, the equation that relates x and y is y = (2/3) * x.
2. For the second set of values, y = 2 and x = 10. Using the formula:
k = 2 / 10 = 1/5
So the constant of proportionality is 1/5.
The equation that relates x and y using this constant becomes:
y = (1/5) * x