Compare Proportions from Graphs & Equations Practice

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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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Answer 1

To determine which graph shows a lower unit cost, we need to understand the slopes of the lines represented by the two graphs. The slope of a line in a coordinate plane often represents a rate, such as cost per unit.

1. Line 1:

   • Passes through (0, 0) and (3, 6).
   • The slope (m) can be calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
   • For Line 1: \( m = \frac{6 - 0}{3 - 0} = \frac{6}{3} = 2 \).

2. Line 2:

   • Passes through (0, 0) and (6, 3).
   • Using the same slope formula:
   • For Line 2: \( m = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2} \).

Now, comparing the slopes:

• Line 1 has a slope of 2, which indicates a cost of 2 units per item.
• Line 2 has a slope of \( \frac{1}{2} \), which indicates a lower cost of \( \frac{1}{2} \) unit per item.

Since a lower slope indicates a lower unit cost, Line 2 shows a lower unit cost compared to Line 1.

Therefore, the answer is: Graph 2 shows a lower unit cost.