Question

Tell whether the set of ordered pairs {(1,1), (3,3), (5,9), (8,13)} satisfies a linear function. Explain

Answer 1

Hello! In order to find a linear function without graphing it, we can see if the x-values (domain) has more than one value of y (range) out of this set of ordered pairs. Those ordered pairs represent a linear function, because each x-value does not have more than 1 y-value. Therefore, those points satisfies a function.

Answer 2

The given set of ordered pairs does not satisfy a linear function.

Given:

The given set of ordered pairs is:

$\{(1,1),(3,3),(5,9),(8,13)\}$

To find:

Whether the given set of ordered pairs satisfies a linear function or not.

Explanation:

Slope of a linear function is:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Slope of linear function passes through the points $(1,1)$ and $(3,3)$ is:

$m_1=\dfrac{3-1}{3-1}$

$m_1=\dfrac{2}{2}$

$m_1=1$

Slope of linear function passes through the points $(3,3)$ and $(5,9)$ is:

$m_2=\dfrac{9-3}{5-3}$

$m_2=\dfrac{6}{2}$

$m_2=3$

Since $m_1\neq m_2$, therefore the given set of ordered pairs does not satisfy a linear function.

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