Decide which of the two given functions is linear and find its equation.

x 0 3 6 10 15
f(x) 0 3 35 57 84
g(x) -1 20 41 69 104

Question

Decide which of the two given functions is linear and find its equation.

x 	0 	3 	6 	10 	15
f(x) 	0 	3 	35 	57 	84
g(x) 	-1    20 	41 	69 	104

anonymous · Answer

second one is

riley · Answer

Did you figure it out just from looking at it??

anonymous · Answer

and you see it because from -1 to 20 is 21 steps and from 20 to 41 is 21 steps

anonymous · Answer

over three, up 21.  also tells you the slope is 7

riley · Answer

oh ever time x increase by 3, g(x) increases by 21

riley · Answer

amg >_< so flipping simple geez . .

anonymous · Answer

exactly.  the change in y has to be constant relative to the change in x.  that is what makes it linear

anonymous · Answer

now you can find the equation with no sweat because not only do you know that the slope is 7 (over 3, up 21) but you are also given that the y-intercept is -1 (0,-1) is on the graph, so equation is 
$$g(x)=7x-1$$

anonymous · Answer

and if need be you can check that 
$$f(10)=7\times 10-1=69$$ as required

anonymous · Answer

bet you wish all math was this easy

riley · Answer

oh thats right because the intercept is the value when x=0 . . . and it says it right there in the table!! wow, thank you again Satellite >.<