Question

On a coordinate plane, line A goes through points (negative 3, 0) and (0, 4), and line B goes through points (0, negative 4) and (2, 0).
Which line has the steeper slope?

Line
has a steeper slope.

Answer 1

To determine which line has the steeper slope, we first need to calculate the slopes of both lines A and B.

**For Line A:**
Line A goes through the points (-3, 0) and (0, 4). The slope (m) can be calculated using the formula:

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

Using the coordinates of the points:
- \( (x_1, y_1) = (-3, 0) \)
- \( (x_2, y_2) = (0, 4) \)

Substituting in the values:

\[
m_A = \frac{4 - 0}{0 - (-3)} = \frac{4}{0 + 3} = \frac{4}{3}
\]

**For Line B:**
Line B goes through the points (0, -4) and (2, 0). Using the same slope formula:

Using the coordinates:
- \( (x_1, y_1) = (0, -4) \)
- \( (x_2, y_2) = (2, 0) \)

Substituting in the values:

\[
m_B = \frac{0 - (-4)}{2 - 0} = \frac{0 + 4}{2} = \frac{4}{2} = 2
\]

**Comparing the slopes:**

- Slope of Line A: \( \frac{4}{3} \) (approximately 1.33)
- Slope of Line B: \( 2 \)

Since \( 2 > \frac{4}{3} \), we can conclude that:

**Line B has a steeper slope.**