Question

suppose that y is directly proportional to x .

1. find the constant of proportionality, k, if y = 10.5 when x = 3 .

write your answer as a decimal.
k =

1. using the k from above write the variation equation in terms of x .

y =

1. using the k from above find y given that x = 28 . write your answer as a decimal.

y =
if needed, round to the nearest tenth.

Explanation:

Step1: Recall direct proportionality formula

If \( y \) is directly proportional to \( x \), the formula is \( y = kx \), where \( k \) is the constant of proportionality.

Step2: Solve for \( k \)

We know \( y = 10.5 \) and \( x = 3 \). Substitute these values into \( y = kx \): \( 10.5 = k \times 3 \). To find \( k \), divide both sides by 3: \( k=\frac{10.5}{3}=3.5 \).

Step3: Write the variation equation

Using \( k = 3.5 \) in \( y = kx \), the equation is \( y = 3.5x \).

Step4: Find \( y \) when \( x = 28 \)

Substitute \( x = 28 \) and \( k = 3.5 \) into \( y = kx \): \( y = 3.5\times28 = 98.0 \).

Answer:

s:

1. \( k = \boldsymbol{3.5} \)
2. \( y = \boldsymbol{3.5x} \)
3. \( y = \boldsymbol{98.0} \)