Noelanijd
2022-07-27
Answered

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

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yatangije62

Answered 2022-07-28
Author has **16** answers

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 $\mathrm{\u25b3}y/\mathrm{\u25b3}x$ 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

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 $\mathrm{\u25b3}y/\mathrm{\u25b3}x$ 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

Answered 2022-07-29
Author has **5** answers

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)

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)

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