Answer:
The rule for the linear function will be:
f(x) = -2x+1
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 as shown in the attached graph
Taking two points
Finding the slope between (0, 1) and (1, -1)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [-1 - 1] / [1 - 0]
= -2 / 1
= -2
Thus, the slope of the line = m = -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 = 1
Thus, the y-intercept b = 1
Now, substituting m = -2 and b = 1 in the slope-intercept form of linear function
y = mx+b
y = (-2)x + 1 ∵ m = -2, b = 1
y = -2x+1
f(x) = -2x+1
Therefore, the rule for the linear function will be:
f(x) = -2x+1
