Question

One of the tables contains (x,y) values that were generated by a linear function. Determine which table, and then write the equation of the linear function represented by the table.

(will attach tables in a sec!)

***PLease explain! Thank youuu :)

Answer 1

Answer choices, table 1,table2,table 3 :)
And idk how to write the equation. Thank you!!

Answer 2

Hi! Thanks for coming! :) Do u understand this? :)

Answer 3

My guess so far would be table 3 tho cuz the differences are constant... am i right about that?

Answer 4

which table has the y values increasing by the sam amount for the same change in x

Answer 5

yeah you got it

Answer 6

okay so my answer for the table is table 3 right?? the others don't work??

Answer 7

how do i plot the coordinates?? and how do i make the equation then?? since table 3 is my choice??

Answer 8

oh okay, and table 1 doesn't work because the y values go +2,+4,+6,+8 etc??
and table 2 is +3,+5,+3,+5 etc?
so we are using table 3?

Answer 9

oh and i need to find the slope first then??

Answer 10

an alternative approach is to take each pair of points and show that the slope between those to pair of points is the same. this implies a linear relationship between them.

Answer 11

okay, so that's what we did with table 3 right? @asnaseer ? we found that the difference for table 3 is constant (x=+2,+2, etc) and (y=+5,+5,+5 etc)

Answer 12

e.g. taking the first two points in table 3, we get the sope as:\[\frac{6-1}{4-2}=\frac{5}{2}\]

Answer 13

so do i just find two random points and find the slope now?

Answer 14

and do i check that for multiple points to make sure the slope is always 5/2??

Answer 15

you should find the slope between each successive pair of points in table 3 remains the same (i.e. 5/2). whereas the slopes between each pair of successive points in tables 1 and 2 do not remain the same.

Answer 16

okay so the slope is 5/2 then?? so far for the equation of the linear function, i have this??
y=5/2x+b ??

Answer 17

you just need to show that the slope remains the same. no need to calculate 'b'

Answer 18

oh but i'm supposed to write the equation of the linear function represented in the table i chose, which was table 3... so how do i write the equation?

Answer 19

and would y=5 then? or no?

Answer 20

oh - sorry - didn't read the whole question :)

Answer 21

since y has a constant difference of 5?

Answer 22

idk hahaa oh it's okay @asnaseer haha :)

Answer 23

what are those @nincompoop?? did u compose the graph/equation of it? idk hahaa if so why? and how'd u get that?

Answer 24

so you had the right idea there, the equation of a straight line is of the form:\[y=mx+b\]where m is the slope and b is the y-intercept.

Answer 25

we showed the slope is 5/2, so you know the equation is of the form:\[y=\frac{5x}{2}+b\]now just stick any point from table 3 into this equation and solve for b.
e.g. you know y=1 when x=2.