Question

Can anyone help me ?

Answer 1

see below

Explanation:

1.

a)

the relation is

`y=5x+28`

b)

`f(x)=5x+28`

we can use it because for every value of x there is just one value, as the definition of function states

c)

`f(22)=?\\\\f(22)=5(22)+28\\\\f(22)=110+28\\\\f(22)=138`

and

`f(?)=128\\\\5x+28=128\\\\5x=128-28\\\\5x=100\\\\x=20`

2.

the points are

(-2,2) with

`x_1=-2\\\\y_1=2`

(1,-3) with

`x_2=1\\\\y_2=-3`

so the change in y is
`y_2-y_1`

`-3-(2)=-5`

and the change in x is
`x_2-x_1`

`1-(-2)=3`

so the slope is

`(\:Change\:in\:y)/(Change\:in\:x) =(-5)/(3) =-(5)/(3)`

and the general formula is

`y=ax+b`

so with a=-5/3

we plug in point 1

`2=-(5)/(3) (-2)+b\\\\2=(10)/(3) +b\\\\6=10+3b\\\\6-10=3b\\\\-4=3b\\\\-(4)/(3)=b`so the formula is

`y=-(5)/(3)x-(4)/(3)`

expressed as a function is

`f(x)=-(5)/(3)x-(4)/(3)`

3.

this is bassically all the work of number 2, so we have

(-2,-5)

`x_1=-2\\\\y_1=-5`

(4,31)

`x_2=4\\\\y_2=31`

so the slope will be

the change in y
`y_2-y_1`

`31-(-5)=36`

the change in x
`x_2-x_1`

`4-(-2)=6`

so the slope will be

`(\Delta\:y)/(\Delta\:x)=(36)/(6) =6` (the triangle means change)

so the formula we have

`y=mx+b\\\\y=6x+b`

we plug some point, let's say 1

`-5=6(-2)+b\\\\-5=-12+b\\\\-5+12=b\\\\7=b`

so the formula is

`y=6x+7`

as a function is

`f(x)=6x+7`

so there you have it

Just as a note, for the next one, put more points :)