Question

find the function rule x:-2, -1, 0, 1, 2 y:9, 4, -1, -6, -11

Answer 1

Well, the pattern is that for each increase of 1 in x, we get a decrease of 5 in y. This resembles a pattern you might know as slope, rise over run. So our "rise" is -5 and our "run" would be 1. This gives a slope of -5. So any function we choose, we want it's slope to be -5.

You may have seen the slope-intercept form equation y = mx + b where m is the slope and b is the y-intercept. Well, from above, we have determined our slope of m to be -5. The y-intercept is the value we get when x = 0. On your list of numbers, x being 0 corresponds to y being -1 (the 3rd number in x pairing with the 3rd number in y). So that means we have a slope of -5 and a y-intercept of -1. This let's us write an equation in y = mx + b form, being y = -5x - 1