Problem:
Let y=mx+b be the image when the line x−3y+11=0 is reflected across the x-axis. The value of m+b is
Answer Choices:
A. −6
B. −5
C. −4
D. −3
E. −2
Solution:
The equation of the given line can be written as y=31​x+311​. The y intercept, b, of the image is −311​ and the slope, m, is −31​. Thus m+b=−4.
OR
If the point (x,y) is on the reflection of the given line, then the point (x,−y) is on the given line. Hence x−3(−y)+11=0, so x+3y=−11 is an equation for the reflected line. The equation of this line can be written y=−31​x−311​, so m+b=−4.