22. Multiple Choice Which of the following lines is the steepest? (4) Line 1: through \( (4,5) \), and \( (3,2) \) (B) Line 2: through \( (6,4) \) and \( (3,2) \) (C) Line 3: through \( (-2,7) \) and \( (6,6) \) (D) Line 4: through \( (-1,3) \) and \( (4,5) \) (E) Line 5: through \( (-2,-4) \) and \( (1,2) \)

To determine which line is the steepest, we need to find the slope of each line. The slope \( m \) is calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). First, let's calculate the slopes for each line: 1) Line 1: Through points \( (4,5) \) and \( (3,2) \): \( m = \frac{2 - 5}{3 - 4} = \frac{-3}{-1} = 3 \) 2) Line 2: Through points \( (6,4) \) and \( (3,2) \): \( m = \frac{2 - 4}{3 - 6} = \frac{-2}{-3} = \frac{2}{3} \) 3) Line 3: Through points \( (-2,7) \) and \( (6,6) \): \( m = \frac{6 - 7}{6 + 2} = \frac{-1}{8} \) 4) Line 4: Through points \( (-1,3) \) and \( (4,5) \): \( m = \frac{5 - 3}{4 + 1} = \frac{2}{5} \) 5) Line 5: Through points \( (-2,-4) \) and \( (1,2) \): \( m = \frac{2 - (-4)}{1 - (-2)} = \frac{2 + 4}{1 + 2} = \frac{6}{3} = 2 \) Now, let's summarize the slopes: - Line 1: \( 3 \) - Line 2: \( \frac{2}{3} \) - Line 3: \( -\frac{1}{8} \) - Line 4: \( \frac{2}{5} \) - Line 5: \( 2 \) The steepest line is Line 1 with a slope of \( 3 \). So the answer is **(A) Line 1**.