Question

Find the constant of variation and write an equation.Y= -6/7 when x= -18/35

Answer 1

Answer:
`\begin{gathered} Equation:\text{ }y\text{ = }(5)/(3)x \\ constant\text{ of variation = 5/3} \end{gathered}`

Step-by-step explanation:

Given:

y varies directly as x

To find:

the equation relating y and x

find the constant of variation when x = -18/35, y = -6/7

We need to write the statement mathematically:

`\begin{gathered} y\text{ }\propto\text{ x} \\ y\text{ = kx} \\ where\text{ k = constant of variation} \end{gathered}`

when x = -18/35, y = -6/7

`\begin{gathered} (-6)/(7)\text{ = k\lparen}(-18)/(35)) \\ \\ (-6)/(7)\text{ = }(-18k)/(35) \\ cross\text{ multiply:} \\ -6(35)\text{ = -18k\lparen7\rparen} \\ -210\text{ = -126k} \end{gathered}`
`\begin{gathered} divide\text{ both sides by -126:} \\ (-210)/(-126)\text{ = }(-126k)/(-126) \\ \\ k\text{ = 1.67 or 1}(2)/(3) \\ constant\text{ of variation is 1}(2)/(3) \end{gathered}`

The equation relating x and y:

`y\text{ = }(5)/(3)x`