The rule for the linear function on the graph is f(x) = 2x - 3.
How to determine the rule of a linear function
To write a rule for a linear function, use the form y = mx + b
where
m is the slope
b is the y-intercept.
Let's determine the slope of function using points (0,-3) and (4,5) on the line.
m = change in y/change in x
m = y₂ - y₁/ x₂ - x₁
m = 5 - (-3)/4 -0
m = 5 + 3/4
m = 8/4 = 2
Slope of the line is 2
Substitute into the general equation of a line
y = mx + b
m = 2
b = y - intercept
= -3
So,
y = 2x - 3
The function f(x) = 2x - 3