y varies directly as x. if y=-5/8 when x=3/2, find x when y=2/5
y = kx
So, y/x = k is a constant.
You want x such that
(-5/8)/(3/2) = (2/5)/x
x = -24/25
To find the value of x when y = 2/5, we can use the concept of direct variation. In direct variation, the relationship between x and y can be expressed using the formula:
y = kx
where k is the constant of variation.
Given that y varies directly as x, we can find the value of k by substituting the given values for y and x into the equation.
Let's substitute y = -5/8 and x = 3/2 into the equation:
-5/8 = k(3/2)
Now, we can solve for k:
k = (-5/8) / (3/2)
= (-5/8) * (2/3)
= -10/24
= -5/12
The constant of variation (k) is -5/12.
Now that we have the value of k, we can find x when y = 2/5 by substituting k and y into the equation:
2/5 = (-5/12) * x
To isolate x, we can multiply both sides of the equation by 12/(-5):
x = (2/5) * (12/(-5))
= (2/1) * (12/(-5))
= 24/(-5)
= -24/5
Therefore, when y = 2/5, the value of x is -24/5.