If you have the following points for X and Y what is the linear function rule?

x = 4, 1

y = 2, -4

I think it is 1/2 x but I'm not sure if it is +6 or - 6

y = mx + b

f(x) = 4m + b = 2
f(x) = m + b = -4

4m + b = 2
-m -b = 4

3 m = 6
m = 2

4(2) + b = 2
8 + b = 2
b = -6

y = 2x - 6

thank you

To find the linear function rule, we can use the formula y = mx + b, where m is the slope of the line and b is the y-intercept.

First, let's find the slope (m) using the given points (x = 4, 1) and (y = 2, -4). The slope formula is:

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

Substituting the values, we get:

m = (-4 - 2) / (1 - 4) = -6 / -3 = 2

The slope (m) of the linear function is 2.

Next, we need to find the y-intercept (b). We can use the formula, y = mx + b, and substitute the values of one of the points, for example, (x = 1, y = -4):

-4 = 2(1) + b
-4 = 2 + b
-6 = b

The y-intercept (b) is -6.

Now, we have the slope (m) as 2 and the y-intercept (b) as -6. Plugging these values into the equation y = mx + b, we get:

y = 2x - 6

Therefore, the linear function rule for the given points is y = 2x - 6.