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.