Final answer:
To check if lines l1 and l2 intersect, compare their slopes and y-intercepts. If the slopes are different, they intersect at one point; if slopes are the same but y-intercepts differ, they are parallel; if both are identical, the lines coincide. To find an intersection point, solve the system of equations representing the lines.
Step-by-step explanation:
To determine whether the lines l1 and l2 intersect, we need to consider their equations in the standard form Ax + By = C. If the lines are represented by their equations, for example, l1: y = mx + b and l2: y = nx + c, where m and n are the slopes and b and c are the y-intercepts, we check for intersection by looking at the slopes and the y-intercepts.
If the slopes m and n are different, the lines intersect at a single point. If the slopes are the same, but the y-intercepts are different, the lines are parallel and do not intersect. However, if both slopes and y-intercepts are the same, the lines are coincident, meaning they lie on top of each other, representing infinite intersections.
To mathematically find the point of intersection, if it exists, we can solve the system of equations formed by the equations of the two lines. This can be done using methods like substitution, elimination, or graphing. Finding the exact point of intersection would involve setting the right-hand sides of the equations equal to each other and solving for x, then substituting this value into either of the original equations to find the corresponding y value.