Answer:
see below
Step-by-step explanation:
1.
a)
the relation is
[tex]y=5x+28[/tex]
b)
[tex]f(x)=5x+28[/tex]
we can use it because for every value of x there is just one value, as the definition of function states
c)
[tex]f(22)=?\\\\f(22)=5(22)+28\\\\f(22)=110+28\\\\f(22)=138[/tex]
and
[tex]f(?)=128\\\\5x+28=128\\\\5x=128-28\\\\5x=100\\\\x=20[/tex]
2.
the points are
(-2,2) with
[tex]x_1=-2\\\\y_1=2[/tex]
(1,-3) with
[tex]x_2=1\\\\y_2=-3[/tex]
so the change in y is [tex]y_2-y_1[/tex]
[tex]-3-(2)=-5[/tex]
and the change in x is [tex]x_2-x_1[/tex]
[tex]1-(-2)=3[/tex]
so the slope is
[tex]\frac{\:Change\:in\:y}{Change\:in\:x} =\frac{-5}{3} =-\frac{5}{3}[/tex]
and the general formula is
[tex]y=ax+b[/tex]
so with a=-5/3
we plug in point 1
[tex]2=-\frac{5}{3} (-2)+b\\\\2=\frac{10}{3} +b\\\\6=10+3b\\\\6-10=3b\\\\-4=3b\\\\-\frac{4}{3}=b[/tex]so the formula is
[tex]y=-\frac{5}{3}x-\frac{4}{3}[/tex]
expressed as a function is
[tex]f(x)=-\frac{5}{3}x-\frac{4}{3}[/tex]
3.
this is bassically all the work of number 2, so we have
(-2,-5)
[tex]x_1=-2\\\\y_1=-5[/tex]
(4,31)
[tex]x_2=4\\\\y_2=31[/tex]
so the slope will be
the change in y [tex]y_2-y_1[/tex]
[tex]31-(-5)=36[/tex]
the change in x [tex]x_2-x_1[/tex]
[tex]4-(-2)=6[/tex]
so the slope will be
[tex]\frac{\Delta\:y}{\Delta\:x}=\frac{36}{6} =6[/tex] (the triangle means change)
so the formula we have
[tex]y=mx+b\\\\y=6x+b[/tex]
we plug some point, let's say 1
[tex]-5=6(-2)+b\\\\-5=-12+b\\\\-5+12=b\\\\7=b[/tex]
so the formula is
[tex]y=6x+7[/tex]
as a function is
[tex]f(x)=6x+7[/tex]
so there you have it
Just as a note, for the next one, put more points :)
