In the xy-coordinate plane, line m is the reflection of line l about the x-axis. If the slope of line m is -4/5, what is the slope of line l?
The slope of the line is the fraction of change of y-coordinate with respect to the change of x coordinate. The slope of -4/5 means that while x changes by 5 units, y changes by -4 units.
After the reflection about the x-axis the line will reflect like a ball in a billiard and for 5 units change in x we will have +4 units change in y. So the new slope will be +4/5.
It looks like this:
\ / line l
/ \ line m
In more sophisticated way you can remember that the slope is tanα, where α is the angle between the line and the x-axis. After the reflection the angle will be −α, and the new slope is tan(−α)=−tanα=−−45=45.