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Airida [17]
3 years ago
15

Can anyone help me ?

Mathematics
1 answer:
Delvig [45]3 years ago
7 0

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}=bso 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 :)

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