Question

Write the rule for the linear function. Remember a function rule is written using f(x)

Answer 1

The rule for the linear function wil be:

• f(x) = x

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

• (0, 0)

• (1, 1)

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:

• f(x) = x