Question

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?

Answer 1

which line for the first answer

Answer 2

LINE A OR C???

Answer 3

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.

Answer 4

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.

Answer 5

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!