Question

Determine whether the lines intersect. If they do, find the point of intersection. If they are skew lines, they are parallel or equal?

1) The lines intersect at a point
2) The lines are skew lines
3) The lines are parallel
4) The lines are equal

Answer 1

Two lines may intersect, be parallel, skew, or equal, determined by their slopes and y-intercepts. Lines with the same slope and y-intercept are equal, while lines with the same slope but different y-intercepts are parallel. Skew lines are not applicable in two-dimensional geometry.

Step-by-step explanation:

To determine if two lines intersect, are parallel, skew, or equal, we must look at their slopes and y-intercepts based on their equations. If two lines have the same slope and the same y-intercept, they are the same line and thus have infinitely many points of intersection. If they have the same slope but different y-intercepts, they are parallel and will never intersect. If their slopes are different, they will intersect at one point, and we can find this point by setting the equations of the lines equal to each other and solving for x and y.

Regarding skew lines, this concept is not applicable to lines in two dimensions (as found in algebra courses) because skew lines exist only in three dimensions or greater, where they do not intersect and are not parallel.

To see if two lines intersect, take for example a line with a slope of 3 and a y-intercept of 9, as given in FIGURE A1. Another line needs to be compared to this one to determine their relationship.