Determine if the equations represent parallel lines, perpendicular lines, or neither.

Question

l1: 5x=10
l2: 6=x

Answer 1

To determine if two lines are parallel, perpendicular, or neither, we can compare the slopes of the two lines.

For equation l1: 5x = 10, we can write this in slope-intercept form: y = mx + b. This is already in this form, with y = 0x + 2 or y = 2. So the slope of l1 is 0.

For equation l2: 6 = x, we can also write this in slope-intercept form: y = mx + b. This can be written as y = 1x + 6, so the slope of l2 is 1.

Since the slope of l1 is 0 and the slope of l2 is 1, these lines are neither parallel nor perpendicular.