The variable y varies inversely as x : y is 1 2/3 when x is -3/5. Find y when x is 3/7
y = k(1/x)
xy = k
when x = -3/5, y = 5/3
(-3/5)(5/3) = k
k = -1
so y = -1/x
xy = -1
if x = 3/7
(3/7)y = -1
y = -7/3
check: (3/7)(-7/3) = -1
To find the value of y when x is 3/7, we can use the inverse variation formula, which states that when two variables are inversely proportional, their product remains constant:
y1 * x1 = y2 * x2.
Here, y1 is the initial value of y when x1 is given, and y2 is the value of y when x2 is given.
Given that y is 1 2/3 when x is -3/5, we can assign these values to y1 and x1:
y1 = 1 2/3 = 5/3,
x1 = -3/5.
Now, we can plug in the values of y1, x1, and x2 into the inverse variation formula and solve for y2:
(5/3) * (-3/5) = y2 * (3/7).
Simplifying the equation:
-1 = (3/7)y2.
To solve for y2, we can multiply both sides of the equation by 7/3:
(-1) * (7/3) = y2.
Doing the calculation:
-7/3 = y2.
Therefore, the value of y when x is 3/7 is -7/3.