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.