$3$ . Determine if each relation is a linear relation or non-linear relation. Explain why. $\newline$ a) $\newline$ \begin{tabular}{|c|c|c|c|c|c|} $\newline$ \hline $x$ & $-4$ & $3$ & $10$ & $17$ & $24$ \\ $\newline$ \hline $y$ & $2$ & $6$ & $10$ & $14$ & $18$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ b) $y=\frac{1}{x}+3$ $\newline$ c) $\newline$ c)

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Math Problems

Grade 8

Domain and range of functions

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3

. Determine if each relation is a linear relation or non-linear relation. Explain why.

\newline

\newline

\begin{tabular}{|c|c|c|c|c|c|}

\newline

\hline

x

-4

3

10

17

24

\newline

\hline

y

2

6

10

14

18

\newline

\hline

\newline

\end{tabular}

\newline

y=\frac{1}{x}+3

\newline

\newline

Check Pattern for Linearity: To determine if the given relations are linear or non-linear, we need to check if they follow a pattern where the change in the dependent variable (usually $y$ ) is constant for every change in the independent variable (usually $x$ ).
Examine Relation a): Let's start with relation a) by examining the given pairs of $x$ and $y$ values: $\newline$ $x$ : $-4$ , $3$ , $10$ , $17$ , $24$ $\newline$ $y$ : $2$ , $y$ $0$ , $10$ , $y$ $2$ , $y$ $3$ $\newline$ We will check if the difference between consecutive $y$ -values is constant as $x$ increases.
Examine Relation b): The differences between consecutive $y$ -values are: $\newline$ $6 - 2 = 4$ $\newline$ $10 - 6 = 4$ $\newline$ $14 - 10 = 4$ $\newline$ $18 - 14 = 4$ $\newline$ Since the difference is constant at $4$ , this suggests that the relation is linear.
No Information for Relation c): Now let's examine relation b) which is given by the equation $y = \frac{1}{x} + 3$ . To determine if this is a linear relation, we need to see if it can be written in the form $y = mx + b$ , where $m$ and $b$ are constants. The equation $y = \frac{1}{x} + 3$ cannot be written in this form because the term $\frac{1}{x}$ is not linear (it is a reciprocal function).
No Information for Relation c): Now let's examine relation b) which is given by the equation $y = \frac{1}{x} + 3$ . To determine if this is a linear relation, we need to see if it can be written in the form $y = mx + b$ , where $m$ and $b$ are constants. The equation $y = \frac{1}{x} + 3$ cannot be written in this form because the term $\frac{1}{x}$ is not linear (it is a reciprocal function).Since the term $\frac{1}{x}$ does not represent a constant rate of change, relation b) is a non-linear relation.
No Information for Relation c): Now let's examine relation b) which is given by the equation $y = \frac{1}{x} + 3$ . To determine if this is a linear relation, we need to see if it can be written in the form $y = mx + b$ , where $m$ and $b$ are constants. The equation $y = \frac{1}{x} + 3$ cannot be written in this form because the term $\frac{1}{x}$ is not linear (it is a reciprocal function).Since the term $\frac{1}{x}$ does not represent a constant rate of change, relation b) is a non-linear relation.For relation c), there is no information provided. We cannot determine if it is linear or non-linear without additional data or an equation.