parallel to line AB containing C

Question

A(14,-2) B (-3,15) C (10,10)

Parallel to line AB containing C?

Answer 1

Elaborating on what Ralph said, first you must determine the slope of AB. Using the rise-run formula, the slope is (15-(-2))/(-3-14) = 17/17 = 1.

The point-slope form of a line is y = mx + b, where m is the slope and b is the y-intercept. Our line connecting A and B, having a slope of 1, should be y = x + b. Because we're looking for a parallel line that goes through C (which is (10, 10)), that parallel line should also have a slope of 1, so it's also in the form of y = x + c, where c is a different constant than that of the line connecting AB.

Now let's plug the values of x and y in:

10 = 10 + c;

c = 0.

Hence, the line we have is y = x.

Answer 2

first figure out slope of line AB. Then use point slope form to figure out equation of line parallel to AB containing C.