Question

Let f be a linear function where f(2)=5 and f(-3)=1 State the function f(x)

Answer 1

I have a function for the first one.
f(x)=3+x
f(2)=5?
Is that a good one?

Answer 2

linear functions are of the form: f(x) = ax+b so if f(2) = 5 means when you plug in 2 to x you get 5, then 2*a+b=5, similarly -3*a+b=1 now solve these: 2*a+b=5 => a=(5-b)/2 and plug it into -3*[(5-b)/2]+b=1 and solve for b,

Answer 3

or you can solve thee two equations simultanesouly and eliminate one of the unknowns, say a, then you can plug the found b value into one of the equations to get a

Answer 4

so mine wouldn't work would it be correct to use two separate equations?

Answer 5

or one single equation

Answer 6

i didnt get the way you found f(x) = 3+x

Answer 7

well here's the thing say we have f(x)=3+x
we plug in f(2)= 3+2 which =5 therefore f(2)=5

Answer 8

but that does not work for f(-3) = 1, if the function were f(x)=3+x then we would expect f(-3) = 3 + (-3) to be 0.

Answer 9

ahh i understand now.

Answer 10

the function should work for any values so the point is: if a function is "linear", just write it of the form ax+b and plug the given values of x and make them equal to the results given.. you'll then have two different equations with a and b in them (because we already replaced xs with the values given) and solve them simultnesouly, find a and b seperately and construct the function such that f(x) = a*x + b

Answer 11

i have a question in your work why is there a negative in the line 2a+b=5

Answer 12

Do you know about slope, you can use that to find the equation of that line. Much easier and a shortcut to the solution

Answer 13

not really

Answer 14

ok, when you write two different equations that way, you should ask yourself which of the unknowns i can eliminate; the easiest way for those equations was to multiply the first one by (-1) and add it to the one below, then we got rid of b's! we found a and plugged the a values to find b

Answer 15

okay i got it soo would this be the equation?