Question

Describe how you would tell that two lines are parallel or coincide by looking at the equations of the lines in standard form.

Answer 1

We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel.

Unlike parallel lines, perpendicular lines do intersect. Their intersection forms a right, or 90-degree, angle.

Answer 2

You can tell if two lines are parallel when they have the same slope but different y-intercept. For example, y = 2x - 4 and y = 2x + 4 would be parallel lines. If they coincide, then the two lines would be on top of each other. For example, first-line with the equation of 3x +3y = 9 and second-line having 9x + 9y = 27 are coinciding lines.