Write a linear function f with f(2)=−2 and f(1)=1.

Answer 1

Hi Quaronna!

First we must realize the following:

f(2) = -2 means that one of the coordinates of this line is (2,-2)

f(1) = 1 means that another coordinate of this line is (1, 1)

This is because the general notation is f(x) = y

Now we use the equation y = mx + b, where we can find the slope, m, and then plug in one of the points to solve for the y-intercept, b

m = y2 - y1 / x2 - x1

m = 1 - (-2) / 1 - 2

m = -3

Arbitrarily choose one of the two coordinates to plug in to find the y-intercept. I chose (1,1) here:

1 = -3(1) + b

b = 4

Therefore, the linear function is y = -3x + 4, or f(x) = -3x + 4