Question

Write an equation for the linear function f with the given values.

1. f(6) = 2 , f(15) = -4

2. f(3) = -.2 , f(.2) = -1.88

Answer 1

x values are your input, y values are your output. with that in mind:

1. (6, 2) and (15, -4) are your points. with two points, you can calculate a slope:

m = (y2 - y1)/(x2 - x1)

m = (-4 - 2)/(15 - 6)
m = (-6)/(9)
m = -2/3

your slope is -2/3.
to get your y-intercept, you need to plug in one of your points into point-slope form:
y - y1 = m(x - x1)
y - 2 = (-2/3)(x - 6)
y - 2 = (-2/3)x + 4
y = (-2/3)x + 6

repeat the same process for number 2.

(3, -.2) and (.2, -1.88)

(-1.88 - - .2)/(.2 - 3)
-1.68/-2.8
m = 0.6

y + .2 = 0.6(x - 3)
y + .2 = 0.6x - 1.8
y = 0.6x - 2