Question

What kind of linear relationship can be represented using a table but not a function? Explain. (1 point)

O A horizontal line can be represented using a table but not a function because the slope is undefined
A vertical line can be represented using a table but not a function because the slope is undefined.
O A vertical line can be represented using a table but not a function because the slope is zero.
O A horizontal line can be represented using a table but not a function because the slope is zero

Answer 1

The correct option is;

A vertical line can be represented using a table but not a function because the slope is undefined

Explanation:

A function, f(x), representing a linear relationship can be presented as follows;

f(x) = m·x + c

Where;

m = The slope = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)

c = The y-intercept

Whereby the line is a vertical line, x₂ = x₁ and x₂ - x₁ =

Therefore;

The slope of a vertical function, m = (y₂ - y₁)/(x₂ - x₁) = (y₂ - y₁)/0 = ∞ from which we have;

f(x) = ∞·x + c = ∞ which is undefined and the vertical line can only be represented using a table but not a function because the slope is undefined