Question

I need help with this please. Can someone help me?

If y=5 when x=-3, find x when y=-1
If y=25 when x=15, find y when x=6

Answer 1

6.
`\displaystyle 10 = y`

5.
`\displaystyle (3)/(5) = x`

Explanation:

You are simply dealing with direct proportional relationships:

`\displaystyle (y)/(6) = (25)/(15); 10 = y`

These are considered equivalent improper fractions. When simplified, you get
`\displaystyle 1(2)/(3).`

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`\displaystyle (-1)/(x) = (5)/(-3); (3)/(5) = x`

If you look closely, you can tell that there is a 1 being used here, and that you need to divide it by the multiplicative inverse of
`\displaystyle (5)/(3),`which is
`\displaystyle (3)/(5),`and sinse both terms are negative integers, you leave the result as is.

I am joyous to assist you at any time.

Answer 2

5. x=0.6 or 3/5 (it's just the fraction and decimal form)

6. y=10

Explanation:

5. We are given y=5 and x=-3, so whenever and need to find x if y=-1

We need to find the "x" for the second proportion

Using this information we can create a ratio or proportion. To understand this better, (usingy=5 and x=-3) we can say that for every 5 of something (y) we have -3 of something (x). We can create a "key" using the proportionality:
`(y)/(x)`

here is our proportion
`(5)/(-3) *(-1)/(x)`

lets cross multiply first, 5x=-1(-3) this simplifies to 5x=3, divide 5 from both sides, 5x/5=3/5 and you x=3/5, so this means that x is 3/5 or 0.6 as decimal

6. Lets set up our "key" again
`(y)/(x)`,

our ratio is for every 25 something (y) we have 15 something(x) or 25/15 or 25:15

`(25)/(15) *(y)/(6)` this is our proportion, lets cross multiply to solve for "y"

25*6=15y this simplifies to 150=15y

lets divide both sides by 15, 150/15-15y/15 and we get our final answer

10=y so our why for this is 10