4. A ray of light travels from the left to along the line x + y = 1 and reflects off the x axis. Write the equation for the reflected ray.
Draw x-y coordinate axes and sketch the ray equation x + y = 1 and the reflection off the x-axis. The reflected ray will be perpendicular to the initial ray.
The slopes of two perpendicular lines are related by: m1 = -1/m2.
Rewrite the first equation to see the slope of the line: y = -x + 1
The slope is -1. The slope of the second line is then: m2 = -1/(-1) = 1.
We have: y = x + b
We need a data point to solve for b. Use the point where the line bounces off the x-axis.
0 = 1 + b b = -1
Then: y = x – 1