An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through four plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma negative 2 right parenthesis, left parenthesis 4 comma negative 4 right parenthesis, and left parenthesis 6 comma negative 6 right parenthesis. The solid line forms the hypotenuse for two triangles. The first triangle is marked with a dotted line and has vertices with coordinates left parenthesis 0 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma negative 2 right parenthesis. The base is labeled as 2, and the perpendicular height on the left is labeled as 2. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 2 comma negative 2 right parenthesis, left parenthesis 2 comma negative 6 right parenthesis, and left parenthesis 6 comma negative 6 right parenthesis. The base is labeled as 4, and the perpendicular height on the left is labeled as 4.

Question

What is the slope of the line?

Answer 1

To find the slope of the line that passes through the points \((0, 0)\) and \((2, -2)\), we can use the slope formula:

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

For the points \((0, 0)\) (where \( x_1 = 0 \) and \( y_1 = 0 \)) and \((2, -2)\) (where \( x_2 = 2 \) and \( y_2 = -2 \)), we substitute into the formula:

\[ \text{slope} = \frac{-2 - 0}{2 - 0} = \frac{-2}{2} = -1 \]

So, the slope of the line is \(-1\).