Problem:
Let y=mx+b be the image when the line xβ3y+11=0 is reflected across the x-axis. The value of m+b is
Answer Choices:
A. β6
B. β5
C. β4
D. β3
E. β2
Solution:
The equation of the given line can be written as y=31βx+311β. The y intercept, b, of the image is β311β and the slope, m, is β31β. Thus m+b=β4.
OR
If the point (x,y) is on the reflection of the given line, then the point (x,βy) is on the given line. Hence xβ3(βy)+11=0, so x+3y=β11 is an equation for the reflected line. The equation of this line can be written y=β31βxβ311β, so m+b=β4.