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 five 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 2 right parenthesis, left parenthesis 2 comma 4 right parenthesis, left parenthesis 3 comma 6 right parenthesis, and left parenthesis 4 comma 8 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 3 comma 0 right parenthesis, and left parenthesis 3 comma 6 right parenthesis. The base is labeled as 3, and the perpendicular height on the right is labeled as 6. The second triangle is marked with a dashed line and has vertices with coordinates left parenthesis 3 comma 6 right parenthesis, left parenthesis 4 comma 6 right parenthesis, and left parenthesis 4 comma 8 right parenthesis. The base is labeled as 1, and the perpendicular height on the right is labeled as 2.

Use similar triangles to determine the slope of the line.

(1 point)
The slope is
Remaining Attempts : 3
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Answer 1

To determine the slope of the line using similar triangles, we can use the information from the triangles described in the illustration.

1. Identify Key Points: The provided points on the line are:

   • (0, 0)
   • (1, 2)
   • (2, 4)
   • (3, 6)
   • (4, 8)

2. Calculate the Slope: The slope \( m \) of a line can be calculated using any two points on the line with the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

   Let's use the points (0, 0) and (4, 8).

   Here:

   • \( y_1 = 0 \), \( y_2 = 8 \)
   • \( x_1 = 0 \), \( x_2 = 4 \)

   Now substitute these values into the slope formula: \[ m = \frac{8 - 0}{4 - 0} = \frac{8}{4} = 2 \]

Therefore, the slope of the line is 2.