Final Answer:
b) The similar triangles show that the slope of the line is -2/3 because The negative slope in the similar triangles implies that the correct answer is (b).
Step-by-step explanation:
The correct answer is (b) - The similar triangles show that the slope of the line is -2/3. In similar triangles, corresponding sides are proportional. The negative sign in the slope indicates a downward direction. Looking at the given options, the correct answer is (b) because the slope is negative, and the ratio is 2/3.
To elaborate, let's consider the concept of similar triangles. Similar triangles have angles that are equal, and their corresponding sides are in proportion. In the given sketch, if the triangles are similar, the ratio of the vertical side to the horizontal side represents the slope of the line. The negative sign indicates the downward direction of the line. Therefore, by analyzing the similar triangles in the sketch, it is evident that the correct slope of the line is -2/3.
In summary, the understanding of similar triangles and the relationship between corresponding sides allows us to determine the slope of the line. The negative slope and the ratio of 2/3 make option (b) the correct choice.