Question

Suppose that f is a linear function with slope 2 and that f(4) = 4. Find the equation for f. (Use x as the variable.)
f(x) = ?

Answer 1

do you know the slope-intercept formula for a line ?

Answer 2

change in f/change in variable ?

Answer 3

that is the definition of slope

have you seen
y= mx + b
?

Answer 4

oh yeah!

Answer 5

do you remember what "m" stands for in
y= mx + b
?

Answer 6

slope?

Answer 7

yes. and what is slope in your problem ?
replace the "m" with the number for the slope
what do you get ?

Answer 8

y=2x+b

Answer 9

next, we use
f(4) = 4

I guess you have to memorize (or learn) that is a way to say
when x is 4 i.e. match f(x) with f(4) to see this)
then y or in this case f(x) is 4

so we put those numbers into

y= 2x + b
4= 2*4 + b

I would simplify 2*4 to 8

4= 8+b

now add -8 to both sides to "solve for b"

Answer 10

stuck ?

Answer 11

yeah

Answer 12

for the moment, assume (4,4) is on the line
y= 2x+b

can you replace x and y with their numbers? what do you get ?

Answer 13

-4 = b?

Answer 14

to get that , you should have put in 4 for y, and 4 for x
and solved
4= 2*4+b
4= 8 + b
4-8 = 8-8+b
-4= b

so the final answer is
y= 2x-4

or
f(x)= 2x-4