help with algebra1 hw!!!! plz???

Question

help me write an equation for this function.

x -2 -1 1 2 4
f(x) 13 12 10 9 7


i really dont get this plz help me!!!!

Answer 1

It helps to see what's going on in between points. From -2 to -1, f(x) goes down 1. From 1 to 2, f(x) again goes down 1. And from 2 to 4, f(x) goes down 2 - which implies that from 2 to 3 and from 3 to 4 f(x) goes down by 1 each time. So from this, it looks like your function is a line, y = mx + b.

Now, how do we figure out m and b (you need to keep x and y in there - that's what makes it a function). m is the slope, and we already see that from point to point, the function changes by 1 - specifically, the function changes by -1. So m = -1.

As for finding b, we can always plug in a set of points (x, y) along with our slope m and calculate b:

y = mx + b
13 = (-1)(-2) + b
13 = 2 + b
b = 11

You could also recall that b is the y-intercept, and from looking at the points, we can see that when x = 0 (we'd be on the y-axis), the value will be 11 - again, from implying this from the way the numbers are laying out.

So your final answer will be y = -x + 11, or f(x) = -x + 11.