Question

A table of values of a linear function is shown below. Find the output when the input is N. Type your answer in the space provide

Answer 1

`-3n - 7`

Explanation:

Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.

Using the slope-intercept formula, y = mx + b, let's find the equation.

Where,

m = the increase in output ÷ increase in input =
`(-13 - (-10))/(2 - 1)`

`m = (-13 + 10)/(1)`

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

`m = -3`

Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept

`y = mx + b`

`-10 = -3(1) + b`

`-10 = -3 + b`

Add 3 to both sides:

`-10 + 3 = -3 + b + 3`

`-7 = b`

`b = -7`

The equation of the given linear function can be written as:

`y = -3x - 7`

Or

`f(x) = -3x - 7`

Therefore, if the input is n, the output would be:

`f(n) = -3n - 7`