Please help me with this homework

(i) Not true for any cases, (ii) True for some cases, (iii) True for some cases, (iv) True for all cases.

Step-by-step explanation:

Now we proceed to check each statement in terms of concepts of function from Analytical Geometry:

(i) Two lines that have the same y-intercept and the same slope intersect at exactly one point.

False, two lines that have the same y-intercept and the same slope intersect at every point. Both lines are coincident. ( Not true for any cases)

(ii) Two lines that have the same y-intercept intersect at exactly one point.

Conditionally true, two lines that have the same y-intercept intersect at exactly one point if and only if slopes are different. ( True for some cases)

(iii) Two lines that have the same slope do not intersect at any point.

Conditionally true, two lines that have the same slope do not intersect at any point if and only if they share the same y-intercept. ( True for some cases)

(iv) Two lines that have two different slopes intersects at exactly one point.

True, two lines that have two different slopes intersects at exactly one point no matter what y-intercepts they have. ( True for all cases)