Question

Question

Use the image to answer the question.

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 1 comma 3 right parenthesis, left parenthesis 2 comma 6 right parenthesis, and left parenthesis 3 comma 9 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 1 comma 0 right parenthesis, and left parenthesis 1 comma 3 right parenthesis. The base is labeled as 1, and the perpendicular height on the right is labeled as 3. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 1 comma 3 right parenthesis, left parenthesis 3 comma 3 right parenthesis, and left parenthesis 3 comma 9 right parenthesis. The base is labeled as 2, and the perpendicular height on the right is labeled as 6.

Use similar triangles to determine the slope of the line.

(1 point)
The slope is

Answer 1

To determine the slope of the line using similar triangles, we can use the coordinates of the points provided. The line passes through the points (0, 0) and (3, 9).

The formula for the slope \( m \) of a line 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 (0, 0) and (3, 9):

• \( x_1 = 0 \)
• \( y_1 = 0 \)
• \( x_2 = 3 \)
• \( y_2 = 9 \)

Now plug in these values:

\[ m = \frac{9 - 0}{3 - 0} = \frac{9}{3} = 3 \]

Therefore, the slope of the line is:

The slope is 3.