Question

Write a linear function f with the values f(0) = 6 and f(4) = -6.

Answer 1

Answer:

f(x) = -3x + 6

Step-by-step explanation:

The general linear function is;

y = mx + b

it can also be written as (x , f(x))

f(x) = mx + b

where m is the slope and b is the y-intercept

so we have the points ;

(0,6) and (4,-6)

So we have;

for f(0) to be 6, it means that the y-intercept b is 6

This is because the value of x at the y-intercept is 0

So we have this as;

f(x) = mx + 6

Now, let’s substitute the other point so as to get m

For the other point;

x = 4 and f(x) = -6

that means;

-6 = 4m + 6

4m = -6-6

4m = -12

m = -12/4

m = -3

So we have the equation as;

f(x) = -3x + 6