Question

The variables x and y vary directly. Use values to write an equation that relates x and y. y=25;x=5And y=20;x=12

Answer 1

A lineal equation has the next form:

`y=mx+b`

where m is the slope and is calculated as follow:

`m=(y_2-y_1)/(x_2-x_1)`

For this case

y1=20

y2= 25

x1=12

x2= 5

so:

`m=\frac{25-20}{5-12_{}}=(5)/(-7)=-(5)/(7)`

then the equation will be:

`y=(-(1)/(7))x+b`

Using one of the points we calculate the b

we are going to use y=25 x=5

`25=(-(5)/(7))5+b`

Clearing the b we get:

`25-(25)/(7)=b\Rightarrow(200)/(7)=b`

b=200/7 or b=28.57

So the final equation is:
`y=-(1)/(7)x+(200)/(7)`