Problem Corner Winter Break 2016/2017

1. How many two-digit numbers are exactly 7 times the sum of their digits?

2. Two straight lines have the same y-intercept and reciprocal slopes. If the first line has slope m and x-intercept a, what is the x-intercept of the other line?

These questions were taken from the Faculty Math League contest at the AMATYC National Conference in Denver. Answers will be posted here.