Given that f(x) is a linear function and f(3) =7 and f(`2)=4,then find f(10).

Question

yatangije62 · Accepted Answer

given that f(x ) is a linear function i can assume that y =mx+B
from there i graph the two points. (2,4) and (3,7) from therei can tell that the slope (m) is equal to 3
slope is

△ y / △ x

or the change in y(3) over the change in x(1)
now that I know that I can solve for B(the constant)
I will use the point (2,4) 4=3(2)+B so B= 4-6 or -2
from there I now can solve for the function of x or y
y = 3x-2
y=3(10)-2 so y=28

Brenton Dixon · Accepted Answer

Well it is first good to know that when they say f(x) the mean"y" and the x in the f(x) really means x. so you have two points on a line given (we know its a line cuz it says linear function).
When f(3) = 7, we know a point on the line ( 3 , 7 )
When f(2) = 4, we know a point on the line ( 2 , 4)
comparing the x's 3 - 2 = 1
comparing the y's 7 - 4 = 3
so the rise over the run is 3/1
now what if x was zero. What would y be? (to find the shift ofthe line)
0 - 2 = -2
so we would have to go 2 left (in the -x direction) to reach this point from the point ( 2 , 4 )
this also means we would go down (in the -y direction) 6.
that would give us the point ( 0 , -2 ) so the shift left would be -2
now we have enough information to create the equation
y = 3x - 2
(ya you can check the other two points, you will find that when you put 2 in for x you get 4. etc)
so putting 10 in for the x
y = 3 (10) -2
y = 28
and we have now found the point ( 10 , 28 )
When f(10) = y, we know a point on the line ( 10 , y)

Given that f(x) is a linear function and f(3) =7 and f(`2)=4,then find f(10).

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