Answer:
The rule for the linear function wil be:
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, 0) and (1, 1)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [1 - 0] / [1 - 0]
= 1 / 1
= 1
Thus, the slope of the line = m = 1
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 = 0
Thus, the y-intercept b = 0
Now, substituting m = 1 and b = 0 in the slope-intercept form of linear function
y = mx+b
y = (1)x + 0 ∵ m = 1, b = 0
y = x
f(x) = x ∵
Therefore, the rule for the linear function wil be:
