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.

1 answer

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.