A straight line passes through points (1, 5) and (6, 0) and intersects with the straight line 2y = 5x – 16 at point P. Find the coordinates of point…

Find the first line through (1, 5) and (6, 0). Slope = (0 − 5)/(6 − 1) = −1. Using (6, 0): y = −(x − 6) = 6 − x.

The second line is 2y = 5x − 16. Put y = 6 − x into it: 12 − 2x = 5x − 16, so 28 = 7x and x = 4.

Then y = 6 − 4 = 2. So P is (4, 2).

Check in the second line: 2(2) = 4 and 5(4) − 16 = 4. ✔