Answer:
f(x) = (1/5)x - (2/5)
Explanation:
The linear function can be written in the form of f(x) = mx + b, where m is the slope and b is the y-intercept.
To find the rule for the linear function when x=-10, y=-1, when x=0, y=1 and when x=10, y=3, we can use the two points method.
We can start by finding the slope (m) of the function using the following formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are two points on the line.
Using the point (-10, -1) and (10, 3) we get:
m = (3 - (-1)) / (10 - (-10)) = 4/20 = 1/5
Now that we know the slope, we can use the point-slope form of the equation of a line to find the equation of the line:
y - y1 = m(x - x1)
Plug in one of the points and the slope that we found:
y - (-1) = (1/5)(x - (-10))
y = (1/5)x - (2/5)
So the equation of the linear function is f(x) = (1/5)x - (2/5)
This is the rule of the linear function when x=-10, y=-1, when x=0, y=1 and when x=10, y=3.