Question

If y=-8 and x= -3 what’s x when y= 6

Answer 1

Part 1)
`x=(9)/(4)`

Part 2)
`x=4`

Explanation:

Analize two problems

Part 1) If y varies directly with x, and If y=-8 and x= -3 what’s x when y= 6

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`k=(y)/(x)` or
`y=kx`

step 1

Find the value of the constant of proportionality k

`k=(y)/(x)`

For x=-3, y=-8

substitute the given values

`k=(-8)/(-3)`

`k=(8)/(3)`

step 2

Find the linear equation

`y=(8)/(3)x`

step 3

Find the value of x when y=6

substitute the value of y in the linear equation

`6=(8)/(3)x`

solve for x

`x=(6)(3)/(8)`

`x=(18)/(8)`

simplify

`x=(9)/(4)`

Part 2) If y varies inversely with x, and If y=-8 and x= -3 what’s x when y= 6

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
`y*x=k` or
`y=k/x`

step 1

Find the value of the constant of proportionality k

`k=y*x`

For x=-3, y=-8

substitute the given values

`k=(-8)(-3)`

`k=24`

step 2

Find the equation

`yx=24`

step 3

Find the value of x when y=6

substitute the value of y in the equation

`6x=24`

solve for x

`x=4`