Question

Help me please i need to get this done

Answer 1

f(x)=2x-1

(the first option)

Explanation:

Linear functions always take the form f(x)=mx+c, where m is the slope and c is the y-intercept.

The y-intercept is the value of y when x is 0, and we can see from the table that when x=0, y=-1. So our value for c is -1.

The slope can be found using the formula
`(y2-y1)/(x2-x1)`, where (x1,y1) and (x2,y2) represent two points that satisy the funciton. Let's talk the first two sets of values for the table to use in this formula - (-5,-11) for (x1,y1) and (0,-1) for (x2,y2) :

m=
`(y2-y1)/(x2-x1)` =
`(-1-(-11))/(0-(-5))`=
`(-1+11)/(0+5)`=
`(10)/(5)`=2

So now we know m=2 and c=-1. Subbing this into f(x)=mx+c and we get:

f(x)=2x-1