Question

write a linear function f with f(2) = -2 and f(1) - 1

f(x) = ?

Answer 1

To find the equation of a linear function, we can use the slope-intercept form: f(x) = mx + b, where m is the slope and b is the y-intercept.

Given f(2) = -2, we can substitute x = 2 into the equation to get -2 = 2m + b.

Similarly, given f(1) = -1, we can substitute x = 1 into the equation to get -1 = m + b.

We now have a system of two equations:

-2 = 2m + b
-1 = m + b

Let's solve this system to find the values of m and b.

From the second equation, we can rearrange it to get b = -1 - m.

Substituting this value of b into the first equation, we get:

-2 = 2m + (-1 - m)
-2 = m - 1
-1 = m

Therefore, m = -1.

Substituting this value of m into the second equation to find b:

-1 = -1 + b
0 = b

Therefore, b = 0.

Now that we know the values of m and b, we can write the equation of the linear function:

f(x) = -x + 0
f(x) = -x