Questions: Graph the equation by plotting points.

Solution Steps

Given the points \((2, -2)\), \((-3, -2)\), and \((1, 0)\), we need to find the equation of the line that passes through these points.

Since the y-values for the first two points are the same, the line is horizontal for these points. However, the third point \((1, 0)\) does not lie on this horizontal line, indicating a different line or a mistake in the problem statement.

Let's assume the line is linear and find the equation using the first and third points: \((2, -2)\) and \((1, 0)\).

The slope \(m\) of the line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Using the points \((2, -2)\) and \((1, 0)\):

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

Using the point-slope form of the equation of a line, \(y - y_1 = m(x - x_1)\), and the point \((2, -2)\):

\[ y - (-2) = -2(x - 2) \]

Simplifying:

\[ y + 2 = -2x + 4 \]

\[ y = -2x + 2 \]

Final Answer