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The four straight lines below are not drawn to the same scale:

Line A: first dot: (3, 9) second dot: (0, 0)
Line B: first dot: (8, 15), second dot: (1, 1)
Line C: first dot: (12, 21), second dot: (3, 3)
Line D: First for: (9, 14), second dot: (1, 2)

Which line is the steepest?

Which two lines are parallel?

5 answers

To determine which line is the steepest and which two lines are parallel, we can calculate the slopes of each line using the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's calculate the slopes for each line:

Line A:

Points: \( (3, 9) \) and \( (0, 0) \)

\[ m_A = \frac{9 - 0}{3 - 0} = \frac{9}{3} = 3 \]

Line B:

Points: \( (8, 15) \) and \( (1, 1) \)

\[ m_B = \frac{15 - 1}{8 - 1} = \frac{14}{7} = 2 \]

Line C:

Points: \( (12, 21) \) and \( (3, 3) \)

\[ m_C = \frac{21 - 3}{12 - 3} = \frac{18}{9} = 2 \]

Line D:

Points: \( (9, 14) \) and \( (1, 2) \)

\[ m_D = \frac{14 - 2}{9 - 1} = \frac{12}{8} = 1.5 \]

Now we have the slopes:

  • \( m_A = 3 \)
  • \( m_B = 2 \)
  • \( m_C = 2 \)
  • \( m_D = 1.5 \)

Conclusion:

  1. The steepest line is Line A with a slope of 3.
  2. The two lines that are parallel are Line B and Line C, as they both have a slope of 2.
which line for the first answer

I apologize if my previous response was unclear. To clarify:

The steepest line, based on the calculated slopes, is Line A, which has a slope of 3.

Thank you for your patience! If you have any more questions or need further assistance, feel free to ask.

LINE A OR C???

Let's carefully re-check the calculations for the slopes to clarify:

  1. Line A: Points (3, 9) and (0, 0) \[ m_A = \frac{9 - 0}{3 - 0} = \frac{9}{3} = 3 \]

  2. Line B: Points (8, 15) and (1, 1) \[ m_B = \frac{15 - 1}{8 - 1} = \frac{14}{7} = 2 \]

  3. Line C: Points (12, 21) and (3, 3) \[ m_C = \frac{21 - 3}{12 - 3} = \frac{18}{9} = 2 \]

  4. Line D: Points (9, 14) and (1, 2) \[ m_D = \frac{14 - 2}{9 - 1} = \frac{12}{8} = 1.5 \]

Summary of Slopes:

  • Line A: \(3\)
  • Line B: \(2\)
  • Line C: \(2\)
  • Line D: \(1.5\)

Conclusion:

  • The steepest line is Line A (slope = 3).
  • Line C (slope = 2) is not steeper than Line A.

So the answer to your question is definitively Line A is the steepest. Thank you for your patience, and I apologize for any confusion earlier!