Answer:
The rule for the linear function will be:
f(x) = 5/2x - 4
Step-by-step explanation:
We know that linear function can be represented using the slope-intercept formula
y = mx+b
where m is the slope and b is the y-intercept
Given the function is linear
Taking two points
Finding the slope between (0, -4) and (2, 1)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [1 - (-4)] / [2 - 0]
= 5 / 2
Thus, the slope of the line = m = 5/2
We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the graph, it is clear
at x = 0, y = -4
Thus, the y-intercept b = -4
Now, substituting m = 5/2 and b = -4 in the slope-intercept form of linear function
y = mx+b
y = (5/2)x + (-4) ∵ m = 5/2, b = -4
y = 5/2x - 4
or
f(x) = 5/2x - 4 ∵ y = f(x)
Therefore, the rule for the linear function will be:
f(x) = 5/2x - 4
