Line 1 and Line 3 are neither parallel nor perpendicular. Slopes: -1, 1/2. Product not -1.
Line 1: Equation is in slope-intercept form (y = mx + b), where m is the slope. Thus, for Line 1, the slope (m1) is -1.
Line 2: Equation is in slope-intercept form, so the slope (m2) is 2.
Line 3: We need to rewrite this equation to slope-intercept form. Divide both sides by 2: y = x + 2.
Now, the slope (m3) is 1/2.
Compare Slopes:
Parallel lines: Two lines are parallel if their slopes are equal.
Perpendicular lines: Two lines are perpendicular if the product of their slopes is -1.
Line 1 and Line 2: m1 * m2 = -1 * 2 = -2 (not equal or -1, so not parallel or perpendicular).
Line 1 and Line 3: m1 * m3 = -1 * (1/2) = -1/2 (not equal or -1, so not parallel or perpendicular).
Result: Neither Line 1 nor Line 3 is parallel or perpendicular to each other.
Complete ques:
Determine the nature of the relationship (parallel, perpendicular, or neither) between each pair of lines given their equations:
Line 1: y = −x+5
Line 2: y = 2x−6
Line 3: 2x−4y = −4