if y varies directly as x, and y=4 when x=12, find y when x=3

Answer 1

If y varies directly as x, then as y increases, x increases also.

Thus, we can set up a proportion as follows:

y_{1 =} y₂

x₁ x₂

Given y = 4 when x = 12, y = ? when x = 3

4 ₌ y₂

12 3 *we can now either cross multiply to solve for y₂ or reduce the fraction on the left side of the proportional equation to solve

cross-multiplying gives:

y₁x₂ = x₁y₂

4(3) = 12y_{2 Substituting given values}

12 = 12y_{2 Simplifying by multiplying}

1 = y_{2 Dividing both sides by 12 to solve for} y₂

reducing fraction gives:

(4/12) reduces to (1/3) because 4 divides both the numerator and denominator of the fraction evenly

Now, (1/3) = (y₂/3) **the denominators of the two equivalent fractions are the same, thus the numerators need to be the same to keep it a true equation

Therefore, y₂ = 1

So in this case when x = 3, y = 1

Hope this helps!

~Jes