suppose y is directly proportional to x. if y=6 when x=4, find the constant of proportionality and write the formula for y as function of x. Use your formula to find x when y=8.
y = kx
6 = 4k, so k = 3/2
y = 3/2 x
To find the constant of proportionality, we can use the given information that y is directly proportional to x. Mathematically, this can be represented as:
y = kx
where k is the constant of proportionality.
Now, let's use the given data point where y = 6 when x = 4 to find the value of k.
Substituting these values into the equation, we get:
6 = k * 4
To solve for k, we divide both sides of the equation by 4:
k = 6/4 = 1.5
So, we have found that the constant of proportionality is k = 1.5.
Now, let's write the formula for y as a function of x:
y = 1.5x
To find x when y = 8, we can substitute y = 8 into the equation and solve for x:
8 = 1.5x
Dividing both sides of the equation by 1.5:
x = 8/1.5 = 5.33 (rounded to 2 decimal places)
Therefore, when y = 8, x ≈ 5.33.
To find the constant of proportionality, we can use the given information that y is directly proportional to x. This means that the ratio between y and x is always constant.
Given:
y = 6 when x = 4
We can use these values to find the constant of proportionality, denoted by k.
Using the formula for direct proportionality, we have:
y = kx
Plugging in the given values, we get:
6 = k * 4
Now, let's solve for k:
k = 6 / 4
k = 1.5
So, the constant of proportionality is 1.5.
Now, we can write the formula for y as a function of x:
y = 1.5x
To find x when y = 8, we can use this formula and substitute the value of y:
8 = 1.5x
Now, we can solve for x:
1.5x = 8
x = 8 / 1.5
x ≈ 5.33
Therefore, when y = 8, x is approximately 5.33.