Question

Can anyone help me ?

Answer 1

Answer:

see below

Step-by-step 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

$\frac{\:Change\:in\:y}{Change\:in\:x} =\frac{-5}{3} =-\frac{5}{3}$

and the general formula is

$y=ax+b$

so with a=-5/3

we plug in point 1

$2=-\frac{5}{3} (-2)+b\\\\2=\frac{10}{3} +b\\\\6=10+3b\\\\6-10=3b\\\\-4=3b\\\\-\frac{4}{3}=b$so the formula is

$y=-\frac{5}{3}x-\frac{4}{3}$

expressed as a function is

$f(x)=-\frac{5}{3}x-\frac{4}{3}$

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

$\frac{\Delta\:y}{\Delta\:x}=\frac{36}{6} =6$                                              (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 :)