Questions: Does the relation represent a Linear function -3 0 6 -3 -1 2

Solution Steps

To determine if a relation represents a linear function, we need to check if the change in the dependent variable (output) is consistent with the change in the independent variable (input). This can be done by calculating the slope between each pair of points and ensuring it remains constant.

The given points are \((-3, -3)\), \((0, -1)\), and \((6, 2)\).

To determine if the relation is linear, calculate the slope between each pair of consecutive points. The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

• Slope between \((-3, -3)\) and \((0, -1)\):

\[ m_1 = \frac{-1 - (-3)}{0 - (-3)} = \frac{2}{3} \]

• Slope between \((0, -1)\) and \((6, 2)\):

\[ m_2 = \frac{2 - (-1)}{6 - 0} = \frac{3}{6} = \frac{1}{2} \]

For the relation to be linear, all calculated slopes must be equal. Here, \(m_1 = \frac{2}{3}\) and \(m_2 = \frac{1}{2}\). Since \(\frac{2}{3} \neq \frac{1}{2}\), the slopes are not equal.

Final Answer