Question

need help please. studying for my final and need someone to remind me how to do these.
for a linear function. f(4)=11 and f(-2)=2. find f(3).

I know that the equation for a linear function is f(x)=mx+b

Answer 1

you have two points : (4, 11) adn (-2, 2)

right ?

Answer 2

f(4) = 11

means

you're sending in x=4, and getting the value y=11 back. that forms a point on the function

Answer 3

so would i try to find m first?

Answer 4

with the given points

Answer 5

you can do it in multiple ways.
i prefer using the two points equation of line :

equation of line passing through (x1, y1) and (x2, y2) :

\(\huge y-y1 = \frac{y2-y1}{x2-x1}(x-x1) \)

Answer 6

equation of line passing thru (4, 11) adn (-2, 2)
\(\huge y-11 = \frac{2-11}{-2-4}(x-4)\)

Answer 7

for m i got 1.5

Answer 8

\(\huge y-11 = 1.5(x-4)\)

Answer 9

\(\huge y-11 = 1.5x-6\)

\(\huge y = 1.5x + 5\)

Answer 10

to find f(3),
plugin x=3 in above equation !

Answer 11

so i only really need to use one set of the points? since i was given (4,11) and (-2,2)

Answer 12

it helps to know equations of lines in 3 forms :
1) slope, intercept form : y = mx+c
2) point, slope form : y-y1 = m(x-x1)
3) two points form : y-y1 = (y2-y1/x2-x1)(x-x1)

Answer 13

we need both points. we used both points to get the equation

Answer 14

but in my case i would be able to use the first one right?

Answer 15

so f(x)=9.5?

Answer 16

*f(3)=9.5

Answer 17

thats right!!

Answer 18

thank you!

Answer 19

yw..