When x = 3, y = 4. What is y when x = 12 if x and y have a proportional relationship?
Please help
To find y when x = 12, if x and y have a proportional relationship, we can use the concept of proportionality or the equation of a line.
Step 1: Determine the proportionality constant (k)
Since x and y have a proportional relationship, we can set up the equation:
x₁ / y₁ = x₂ / y₂
where x₁ = 3, y₁ = 4, x₂ = 12, and y₂ is what we need to find.
Substituting the values, we have:
3 / 4 = 12 / y₂
Step 2: Solve for y₂
To isolate y₂, cross-multiply the ratio:
3 / 4 * y₂ = 12
Now, multiply both sides by 4 to eliminate the fraction:
3 * y₂ = 48
Step 3: Solve for y₂
Divide both sides of the equation by 3 to solve for y₂:
y₂ = 48 / 3
Simplifying the expression:
y₂ = 16
So, when x = 12, y is equal to 16.
To find the value of y when x = 12, we need to determine the proportionality constant or the ratio between x and y.
In a proportional relationship, the ratio between x and y should remain constant. We can find this constant by taking the ratio of the given values of x and y.
Given:
x = 3, y = 4
The ratio of x to y at this point is:
3 / 4
Now, we can use this ratio to find y when x = 12.
Multiply the ratio by 12:
(3 / 4) * 12 = 9
So, when x = 12, y equals 9.
Therefore, when x = 12 in a proportional relationship, y is equal to 9.
y = kx
so, 4 = 3k ... k = 4/3
so now you can find y when x=12