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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. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, 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 B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, 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 objects is moving at a rate of 2 feet per second?

(1 point)

1 answer

To determine which line represents an object moving at a rate of 2 feet per second, we need to calculate the slope of each line labeled A, B, and C. The slope (rate) can be calculated using the formula:

\[ \text{slope} = \frac{\text{change in distance}}{\text{change in time}} = \frac{y_2 - y_1}{x_2 - x_1} \]

  1. Line A: Passes through (0, 0) and (3, 6) \[ \text{slope A} = \frac{6 - 0}{3 - 0} = \frac{6}{3} = 2 \text{ feet per second} \]

  2. Line B: Passes through (0, 0) and (6, 6) \[ \text{slope B} = \frac{6 - 0}{6 - 0} = \frac{6}{6} = 1 \text{ foot per second} \]

  3. Line C: Passes through (0, 0) and (6, 3) \[ \text{slope C} = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2} \text{ feet per second} \]

Based on these calculations, Line A is moving at a rate of 2 feet per second.