Question

Suppose that y is directly proportional to x. Find the constant of proportionality k if y = 5.2 when x = 4. (Write your antwer as a decimal.) Using the k from above write the variation equation in terms of x. y = Using the k from above find y given that x = 28. y = If needed, round answer to 3 decimal places. Enter DNE for Does Not Exist, oo for Infinity D Video

Answer 1

From the statement of the problem we know that y is proportional to x, so the equation of y in terms of the variable x, constitutes a linear equation of the form:

`y=k\cdot x`

Where k is the slope.

1) We also know that for y = 5.2 the variable x takes the value x = 4, replacing these in the equation above we have:

`\begin{gathered} 5.2=k\cdot4 \\ k=(5.2)/(4) \\ k=1.3 \end{gathered}`

2) Replacing the value of k in the first equation we get:

`y=1.3\cdot x`

3) Now, given the last equation and a value x = 28 we find the value for y:

`\begin{gathered} y=1.3\cdot28 \\ y=36.4 \end{gathered}`

In summary, the answers are:

`\begin{gathered} k=1.3 \\ y=1.3x \\ y=36.4 \end{gathered}`