Question

The equation x - 2y = 15 describes line 1. The equation y = -2x + 3 describes line 2. Which statement is true?

A. Line 1 is parallel to line 2.

B. Line 1 is perpendicular to line 2.

C. Line 1 is neither parallel nor perpendicular to line 2.

Answer 1

Line 1 is perpendicular to line 2.

Step-by-step explanation:

To determine whether line 1 and line 2 are parallel or perpendicular, we need to examine their slopes. Line 1 has the equation x - 2y = 15. We can rearrange this equation to solve for y: y = (1/2)x - 15/2. The slope of line 1 is (1/2), which means it has a positive slope. Line 2 has the equation y = -2x + 3, which is in slope-intercept form. The slope of line 2 is -2, which means it has a negative slope. Since the slopes of the two lines are different and have opposite signs, line 1 and line 2 are perpendicular. Therefore, the correct statement is B. Line 1 is perpendicular to line 2.