Write the rule for the linear function. Remember a function rule is written using

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

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