Use the image to answer the question.

Question

An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. A solid line, labeled 1, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled 2, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.

Which of these graphs shows a lower unit cost, 1 or 2?(1 point)
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Remaining

Answer 1

To determine which graph shows a lower unit cost, we need to analyze the slopes of the lines based on their coordinates:

1. Line 1 has endpoints at (0, 0) and (3, 6).

   • The slope (m) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 0}{3 - 0} = \frac{6}{3} = 2 \]
   • This means for every unit increase along the x-axis, there is a corresponding increase of 2 units on the y-axis.

2. Line 2 has endpoints at (0, 0) and (6, 3).

   • The slope (m) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2} \]
   • This means for every unit increase along the x-axis, there is a corresponding increase of only 0.5 units on the y-axis.

Since a lower slope indicates a lower unit cost, Line 2 (with a slope of 0.5) shows a lower unit cost than Line 1 (with a slope of 2).

Therefore, the graph that shows a lower unit cost is Line 2.