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 will be:

`f(x) = -2x+5`

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 from the table to determine the slope

• (1, 3)

• (2, 1)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(1,\:3\right),\:\left(x_2,\:y_2\right)=\left(2,\:1\right)`

`m=(1-3)/(2-1)`

`m=-2`

Using the point-slope form of the line equation

`y-y_1=m\left(x-x_1\right)`

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (1, 3)

`y-y_1=m\left(x-x_1\right)`

`y - 3 = -2 (x-1)`

`y-3 = -2x+2`

adding 3 to both sides

`y-3+3 = -2x+2+3`

`y = -2x+5`

or

`f(x) = -2x+5`

Therefore, the rule for the linear function will be:

`f(x) = -2x+5`